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1. Introduction - probably refrasing about the "assumption"
2. Definitions of the Knowledge and Evidence + explanation about what is "production of Knolwedge" and "How we can accept the conclusion beyond evidence"
3. Implications
a. knowledge can be produced
b. we must assume something to produce knowledge
c. Conclusion can exist beyond evidence
d.

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is accepting knolwedge is faith.

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The scientific acceptance of mathematical evidence from theoretical physicist. 

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The scientific acceptance of mathematical evidence from theoretical physicist. 

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The higgs theory

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1. Knowledge. how is this produced.
2. Is it need to be true?
3. evidence. What is evidence
4. how valid / reliable is it need to be. What WOK is considered to be the main source of evidence?
5. example of the cases of AOK not following the statment.
6. following statment.

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The term has subtle differences in definition when used in the context of different fields of study. As defined in classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. As used in modern logic, an axiom is simply a premise or starting point for reasoning.

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- Production of knowledge requires accepting conclusions beyond evidence

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Production of knoweldge --> the problem of the accepting wrong conclusion. 

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Production of knoweldge --> the problem of the accepting wrong conclusion. 

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The believe in the things not existing

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Role of authority in the production of knw

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Role of authority in the production of knw

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used for the natural / human science.

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Error analysis (mathematics) - Wikipedia

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In mathematics, error analysis is the study of kind and quantity of error, or uncertainty, that may be present in the solution to a problem. This issue is particularly prominent in applied areas such as numerical analysis and statistics.

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"Production of knowledge"
"Accepting conclusions" "Beyond evidence."

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My science is at home...

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Definition of evidence: the available body of facts or information indicating whether a belief or proposition is true or valid.

Whether we want valide knowledge or reliable knowledge for evidence is dffierent by each AOK.

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Learning Objectives

1. Define reliability, including the different types and how they are assessed.

2. Define validity, including the different types and how they are assessed.

3. Describe the kinds of evidence that would be relevant to assessing the reliability and validity of a particular measure.

Again, measurement involves assigning scores to individuals so that they represent some characteristic of the individuals. But how do researchers know that the scores actually represent the characteristic, especially when it is a construct like intelligence, self-esteem, depression, or working memory capacity? The answer is that they conduct research using the measure to confirm that the scores make sense based on their understanding of the construct being measured. This is an extremely important point. Psychologists do not simply assume that their measures work. Instead, they collect data to demonstrate that they work. If their research does not demonstrate that a measure works, they stop using it.

As an informal example, imagine that you have been dieting for a month. Your clothes seem to be fitting more loosely, and several friends have asked if you have lost weight. If at this point your bathroom scale indicated that you had lost 10 pounds, this would make sense and you would continue to use the scale. But if it indicated that you had gained 10 pounds, you would rightly conclude that it was broken and either fix it or get rid of it. In evaluating a measurement method, psychologists consider two general dimensions: reliability and validity.

Reliability

Reliability refers to the consistency of a measure. Psychologists consider three types of consistency: over time (test-retest reliability), across items (internal consistency), and across different researchers (inter-rater reliability).

Test-Retest Reliability

When researchers measure a construct that they assume to be consistent across time, then the scores they obtain should also be consistent across time. Test-retest reliability is the extent to which this is actually the case. For example, intelligence is generally thought to be consistent across time. A person who is highly intelligent today will be highly intelligent next week. This means that any good measure of intelligence should produce roughly the same scores for this individual next week as it does today. Clearly, a measure that produces highly inconsistent scores over time cannot be a very good measure of a construct that is supposed to be consistent.

Assessing test-retest reliability requires using the measure on a group of people at one time, using it again on the same group of people at a later time, and then looking at test-retest correlation between the two sets of scores. This is typically done by graphing the data in a scatterplot and computing Pearson's r. Figure 5.2 shows the correlation between two sets of scores of several university students on the Rosenberg Self-Esteem Scale, administered two times, a week apart. Pearson's r for these data is +.95. In general, a test-retest correlation of +.80 or greater is considered to indicate good reliability.

Again, high test-retest correlations make sense when the construct being measured is assumed to be consistent over time, which is the case for intelligence, self-esteem, and the Big Five personality dimensions. But other constructs are not assumed to be stable over time. The very nature of mood, for example, is that it changes. So a measure of mood that produced a low test-retest correlation over a period of a month would not be a cause for concern.

Internal Consistency

A second kind of reliability is internal consistency, which is the consistency of people's responses across the items on a multiple-item measure. In general, all the items on such measures are supposed to reflect the same underlying construct, so people's scores on those items should be correlated with each other. On the Rosenberg Self-Esteem Scale, people who agree that they are a person of worth should tend to agree that that they have a number of good qualities. If people's responses to the different items are not correlated with each other, then it would no longer make sense to claim that they are all measuring the same underlying construct. This is as true for behavioural and physiological measures as for self-report measures. For example, people might make a series of bets in a simulated game of roulette as a measure of their level of risk seeking. This measure would be internally consistent to the extent that individual participants' bets were consistently high or low across trials.

Like test-retest reliability, internal consistency can only be assessed by collecting and analyzing data. One approach is to look at a split-half correlation. This involves splitting the items into two sets, such as the first and second halves of the items or the even- and odd-numbered items. Then a score is computed for each set of items, and the relationship between the two sets of scores is examined. For example, Figure 5.3 shows the split-half correlation between several university students' scores on the even-numbered items and their scores on the odd-numbered items of the Rosenberg Self-Esteem Scale. Pearson's r for these data is +.88. A split-half correlation of +.80 or greater is generally considered good internal consistency.

Perhaps the most common measure of internal consistency used by researchers in psychology is a statistic called Cronbach's α (the Greek letter alpha). Conceptually, α is the mean of all possible split-half correlations for a set of items. For example, there are 252 ways to split a set of 10 items into two sets of five. Cronbach's α would be the mean of the 252 split-half correlations. Note that this is not how α is actually computed, but it is a correct way of interpreting the meaning of this statistic. Again, a value of +.80 or greater is generally taken to indicate good internal consistency.

Interrater Reliability

Many behavioural measures involve significant judgment on the part of an observer or a rater. Inter-rater reliability is the extent to which different observers are consistent in their judgments. For example, if you were interested in measuring university students' social skills, you could make video recordings of them as they interacted with another student whom they are meeting for the first time. Then you could have two or more observers watch the videos and rate each student's level of social skills. To the extent that each participant does in fact have some level of social skills that can be detected by an attentive observer, different observers' ratings should be highly correlated with each other. Inter-rater reliability would also have been measured in Bandura's Bobo doll study. In this case, the observers' ratings of how many acts of aggression a particular child committed while playing with the Bobo doll should have been highly positively correlated. Interrater reliability is often assessed using Cronbach's α when the judgments are quantitative or an analogous statistic called Cohen's κ (the Greek letter kappa) when they are categorical.

Validity

Validity is the extent to which the scores from a measure represent the variable they are intended to. But how do researchers make this judgment? We have already considered one factor that they take into account-reliability. When a measure has good test-retest reliability and internal consistency, researchers should be more confident that the scores represent what they are supposed to. There has to be more to it, however, because a measure can be extremely reliable but have no validity whatsoever. As an absurd example, imagine someone who believes that people's index finger length reflects their self-esteem and therefore tries to measure self-esteem by holding a ruler up to people's index fingers. Although this measure would have extremely good test-retest reliability, it would have absolutely no validity. The fact that one person's index finger is a centimetre longer than another's would indicate nothing about which one had higher self-esteem.

Discussions of validity usually divide it into several distinct "types." But a good way to interpret these types is that they are other kinds of evidence-in addition to reliability-that should be taken into account when judging the validity of a measure. Here we consider three basic kinds: face validity, content validity, and criterion validity.

Face Validity

Face validity is the extent to which a measurement method appears "on its face" to measure the construct of interest. Most people would expect a self-esteem questionnaire to include items about whether they see themselves as a person of worth and whether they think they have good qualities. So a questionnaire that included these kinds of items would have good face validity. The finger-length method of measuring self-esteem, on the other hand, seems to have nothing to do with self-esteem and therefore has poor face validity. Although face validity can be assessed quantitatively-for example, by having a large sample of people rate a measure in terms of whether it appears to measure what it is intended to-it is usually assessed informally.

Face validity is at best a very weak kind of evidence that a measurement method is measuring what it is supposed to. One reason is that it is based on people's intuitions about human behaviour, which are frequently wrong. It is also the case that many established measures in psychology work quite well despite lacking face validity. The Minnesota Multiphasic Personality Inventory-2 (MMPI-2) measures many personality characteristics and disorders by having people decide whether each of over 567 different statements applies to them-where many of the statements do not have any obvious relationship to the construct that they measure. For example, the items "I enjoy detective or mystery stories" and "The sight of blood doesn't frighten me or make me sick" both measure the suppression of aggression. In this case, it is not the participants' literal answers to these questions that are of interest, but rather whether the pattern of the participants' responses to a series of questions matches those of individuals who tend to suppress their aggression.

Content Validity

Content validity is the extent to which a measure "covers" the construct of interest. For example, if a researcher conceptually defines test anxiety as involving both sympathetic nervous system activation (leading to nervous feelings) and negative thoughts, then his measure of test anxiety should include items about both nervous feelings and negative thoughts. Or consider that attitudes are usually defined as involving thoughts, feelings, and actions toward something. By this conceptual definition, a person has a positive attitude toward exercise to the extent that he or she thinks positive thoughts about exercising, feels good about exercising, and actually exercises. So to have good content validity, a measure of people's attitudes toward exercise would have to reflect all three of these aspects. Like face validity, content validity is not usually assessed quantitatively. Instead, it is assessed by carefully checking the measurement method against the conceptual definition of the construct.

Criterion Validity

Criterion validity is the extent to which people's scores on a measure are correlated with other variables (known as criteria) that one would expect them to be correlated with. For example, people's scores on a new measure of test anxiety should be negatively correlated with their performance on an important school exam. If it were found that people's scores were in fact negatively correlated with their exam performance, then this would be a piece of evidence that these scores really represent people's test anxiety. But if it were found that people scored equally well on the exam regardless of their test anxiety scores, then this would cast doubt on the validity of the measure.

A criterion can be any variable that one has reason to think should be correlated with the construct being measured, and there will usually be many of them. For example, one would expect test anxiety scores to be negatively correlated with exam performance and course grades and positively correlated with general anxiety and with blood pressure during an exam. Or imagine that a researcher develops a new measure of physical risk taking. People's scores on this measure should be correlated with their participation in "extreme" activities such as snowboarding and rock climbing, the number of speeding tickets they have received, and even the number of broken bones they have had over the years. When the criterion is measured at the same time as the construct, criterion validity is referred to as concurrent validity; however, when the criterion is measured at some point in the future (after the construct has been measured), it is referred to as predictive validity (because scores on the measure have "predicted" a future outcome).

Criteria can also include other measures of the same construct. For example, one would expect new measures of test anxiety or physical risk taking to be positively correlated with existing measures of the same constructs. This is known as convergent validity.

Assessing convergent validity requires collecting data using the measure. Researchers John Cacioppo and Richard Petty did this when they created their self-report Need for Cognition Scale to measure how much people value and engage in thinking (Cacioppo & Petty, 1982). In a series of studies, they showed that people's scores were positively correlated with their scores on a standardized academic achievement test, and that their scores were negatively correlated with their scores on a measure of dogmatism (which represents a tendency toward obedience). In the years since it was created, the Need for Cognition Scale has been used in literally hundreds of studies and has been shown to be correlated with a wide variety of other variables, including the effectiveness of an advertisement, interest in politics, and juror decisions (Petty, Briñol, Loersch, & McCaslin, 2009).

Discriminant Validity

Discriminant validity, on the other hand, is the extent to which scores on a measure are not correlated with measures of variables that are conceptually distinct. For example, self-esteem is a general attitude toward the self that is fairly stable over time. It is not the same as mood, which is how good or bad one happens to be feeling right now. So people's scores on a new measure of self-esteem should not be very highly correlated with their moods. If the new measure of self-esteem were highly correlated with a measure of mood, it could be argued that the new measure is not really measuring self-esteem; it is measuring mood instead.

When they created the Need for Cognition Scale, Cacioppo and Petty also provided evidence of discriminant validity by showing that people's scores were not correlated with certain other variables. For example, they found only a weak correlation between people's need for cognition and a measure of their cognitive style-the extent to which they tend to think analytically by breaking ideas into smaller parts or holistically in terms of "the big picture." They also found no correlation between people's need for cognition and measures of their test anxiety and their tendency to respond in socially desirable ways. All these low correlations provide evidence that the measure is reflecting a conceptually distinct construct.

Key Takeaways

Psychological researchers do not simply assume that their measures work. Instead, they conduct research to show that they work. If they cannot show that they work, they stop using them.

There are two distinct criteria by which researchers evaluate their measures: reliability and validity. Reliability is consistency across time (test-retest reliability), across items (internal consistency), and across researchers (interrater reliability). Validity is the extent to which the scores actually represent the variable they are intended to.

Validity is a judgment based on various types of evidence. The relevant evidence includes the measure's reliability, whether it covers the construct of interest, and whether the scores it produces are correlated with other variables they are expected to be correlated with and not correlated with variables that are conceptually distinct.

The reliability and validity of a measure is not established by any single study but by the pattern of results across multiple studies. The assessment of reliability and validity is an ongoing process.

Exercises

1. Practice: Ask several friends to complete the Rosenberg Self-Esteem Scale. Then assess its internal consistency by making a scatterplot to show the split-half correlation (even- vs. odd-numbered items). Compute Pearson's r too if you know how.

2. Discussion: Think back to the last college exam you took and think of the exam as a psychological measure. What construct do you think it was intended to measure? Comment on its face and content validity. What data could you collect to assess its reliability and criterion validity?

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Define reliability, including the different types and how they are assessed. Define validity, including the different types and how they are assessed. Describe the kinds of evidence that would be relevant to assessing the reliability and validity of a particular measure. Again, measurement involves assigning scores to individuals so that they represent some characteristic of the individuals.

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History.
without historical evidence, the knowledge can't be produced. Accepting conclusion not based on evidence is not acceptable.

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To know of anything we accept into our memory details, concepts, even just a purely abstract idea can be taken into a persons memory - something like mathematics might fall into this category, something without real substance or form can be known.

We can, through language, spread our knowledge far easier than any species before us was able to do so, we are a species of knowledge that spans generations.
Now, what is 'truth' ?
I put forward that "truth", "that which is true", is something which is accurate to our observable world, by contrast that which is not true does not withstand much scrutiny and with investigation can be found to be a falsehood.
Is all knowledge truthful?
Let me express this answer through metaphor and understandable details;

1 - I know of unicorns, I can accurately describe one, I can recall how a unicorn would be expected to behave, I have quite vast and in depth knowledge of unicorns.

2 - I know how to build a computer from components, I can detail each part, tell you what it does and I can show you with some accuracy how it all fits together.

3 - I know some basic web coding, I can tell you some of the terminology used, what it does, and even give a practical demonstration of what bits I know of.

In the first example: unicorns are a fantasy, their existence is a falsehood, it it not true, and yet I know of it. If I ask you to fetch me a unicorn horn.. you'd never succeed. I know of such an animal, but it is not truth.

In the third example, my knowledge of computers is based on my interaction with actual computer components, these things are true and real in the world, I can hand you a graphics card and you can inspect it, it exists. I know of these things and they are true.

In the last example, my intangible knowledge of coding is true even though it has no substance (except perhaps the parts of my brain in which those memories are kept) for you to hold, I cannot ask you to weigh my CSS knowledge, but I can demonstrate it, I can perform tasks in reality which are governed by that knowledge. Although it is an abstract it is true.
A small mind game for you:
You and I have never met, nor are we likely to. If I now tell you that I always wear a lime-green t-shirt, I have bright, almost white, blonde hair, I can speak German fluently and I'm an active participant of a local Tai-chi group.

Is any of that true?
Is some of it true?
Is it all true?

You now know these things, these details are now your knowledge... but is your knowledge the truth?
My conclusion
Not all knowledge is truthful, simply because we can know of something does not mean that thing is true within the reality in which we live our lives. We have incredible minds and sadly these incredible tools are capable of accepting lies as though they are truths.

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Does knowledge have to be true in order for it to be knowledge?

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Answer (1 of 3): Does knowledge have to be true in order for it to be knowledge? "True" is a slippery term, meaning different things for different people. I prefer "fact." A fact is something that just is, like a tree or a rock. You can't dispute its reality.

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Differentiate Among Empirical, Anecdotal, and Logical Evidence (English II Reading) | Texas Gateway

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- by each WOK, the evidence can be different.
1. logical evience
2. emotional evidence
3. Sensory evidence
4. memory based
5. intuitive evidence
6. imaginative evidence.

each sections has the different level of validity. Logical evidence is the most acceptable / intuitive and emotion is less acceptable.

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AOK agreeing
- Natural / Human science
- some evidences must be generalized in order to be applied. (although it is experimented in very high precision.)(inductive reasonings)
- History
- Can't have historical evidence of every moment --> some most be infered. the knoweldge beyond evidence.

AOK disagreeing
- Art
- Mathematics
- can't assume something beyond the logic. (there are no evidence for math. only logic exist.)

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Older blog post: This text is a loose continuation of the 2007 essay on Zeta function regularization

Dear perplexed, there are many ways to see that your result is the right one. What does it mean the right one?

It means that whenever such a sum appears anywhere in physics - I explicitly emphasize that not just in string theory, also in experimentally doable measurements of the [ Casimir force][1] (between parallel metals resulting from quantized standing electromagnetic waves in between) - and one knows that the result is finite, the only possible finite part of the result that may be consistent with other symmetries of the problem (and that is actually confirmed experimentally whenever it is possible) is equal to $$$-1/12$$$.

It's another widespread misconception (see all the incorrect comments right below your question) that the zeta-function regularization is the only way how to calculate the proper value. Let me show a completely different calculation - one that is a homework exercise in Joe Polchinski's "String Theory" textbook.

Exponential regulator method

Add an exponentially decreasing regulator to make the sum convergent - so that the sum becomes
$$ S = \sum_{n=1}^{\infty} n e^{-\epsilon n} $$
Note that this is not equivalent to generalizing the sum to the zeta-function. In the zeta-function, the $$$n$$$ is the base that is exponentiated to the $$$s$$$th power. Here, the regulator has $$$n$$$ in the exponent. Obviously, the original sum of integers is obtained in the $$$\epsilon\to 0$$$ limit of the formula for $$$S$$$. In physics, $$$\epsilon$$$ would be viewed as a kind of "minimum distance" that can be resolved.

The sum above may be exactly evaluated and the result is (use Mathematica if you don't want to do it yourself, but you can do it yourself)
$$ S = \frac{e^\epsilon}{(e^\epsilon-1)^2} $$
We will only need some Laurent expansion around $$$\epsilon = 0$$$.
$$ S = \frac{1+\epsilon+\epsilon^2/2 + O(\epsilon^3)}{(\epsilon+\epsilon^2/2+\epsilon^3/6+O(\epsilon^4))^2} $$
We have
$$ S = \frac{1}{\epsilon^2} \frac{1+\epsilon+\epsilon^2/2+O(\epsilon^3)}{(1+\epsilon/2+\epsilon^2/6+O(\epsilon^3))^2} $$
You see that the $$$1/\epsilon^2$$$ leading divergence survives and the next subleading term cancels. The resulting expansion may be calculated with this Mathematica command

1/epsilon^2 * Series[epsilon^2 Sum[n Exp[-n epsilon], {n, 1, Infinity}], {epsilon, 0, 5}]

and the result is
$$ \frac{1}{\epsilon^2} - \frac{1}{12} + \frac{\epsilon^2}{240} + O(\epsilon^4) $$
In the $$$\epsilon\to 0$$$ limit we were interested in, the $$$\epsilon^2/240$$$ term as well as the smaller ones go to zero and may be erased. The leading divergence $$$1/\epsilon^2$$$ may be and must be canceled by a local counterterm - a vacuum energy term. This is true for the Casimir effect in electromagnetism (in this case, the cancelled pole may be interpreted as the sum of the zero-point energies in the case that no metals were bounding the region), zero-point energies in string theory, and everywhere else. The cancellation of the leading divergence is needed for physics to be finite - but one may guarantee that the counterterm won't affect the finite term, $$$-1/12$$$, which is the correct result of the sum.

In physics applications, $$$\epsilon$$$ would be dimensionful and its different powers are sharply separated and may be treated individually. That's why the local counterterms may eliminate the leading divergence but don't affect the finite part. That's also why you couldn't have used a more complex regulator, like $$$\exp(-(\epsilon+\epsilon^2)n)$$$.

There are many other, apparently inequivalent ways to compute the right value of the sum. It is not just the zeta function.

Euler's method

Let me present one more, slightly less modern, method that was used by Leonhard Euler to calculate that the sum of integers is $$$-1/12$$$. It's of course a bit more heuristic but his heuristic approach showed that he had a good intuition and the derivation could be turned into a modern physics derivation, too.

We will work with two sums,
$$ \begin{align} S &= 1+2+3+4+5+\dots, \\ \quad T &= 1-2+3-4+5-\dots \end{align} $$
Extrapolating the geometric and similar sums to the divergent (and, in this case, marginally divergent) domain of values of $$$x$$$, the expression $$$T$$$ may be summed according to the Taylor expansion
$$ \frac{1}{(1+x)^2} = 1 - 2x + 3x^2 -4x^3 + \dots $$
Substitute $$$x=1$$$ to see that $$$T=+1/4$$$. The value of $$$S$$$ is easily calculated now:
$$ \begin{align}T &= (1+2+3+\dots) - 2\times (2+4+6+\dots)= \\ &= (1+2+3+\dots) (1 - 4) =\\ &= -3S \end{align} $$
so $$$S=-T/3=-1/12$$$.

A zeta-function calculation

A somewhat unusual calculation of $$$\zeta(-1)=-1/12$$$ of mine may be found here:

The comments are in Czech but the equations represent bulk of the language that really matters, so the Czech comments shouldn't be a problem. A new argument (subscript) $$$s$$$ is added to the zeta function. The new function is the old zeta function for $$$s=0$$$ and for $$$s=1$$$, it only differs by one. We Taylor expand around $$$s=0$$$ to get to $$$s=1$$$ and we find out that only a finite number of terms survives if the main argument $$$x$$$ is a non-positive integer. The resulting recursive relations for the zeta function allow us to compute the values of the zeta-function at integers smaller than $$$1$$$, and prove that the function [ vanishes][2] at negative even values of $$$x$$$.

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high-energy particle string theory supersymmetry gluino quantum theory m-theory science global warming definition lhc libertarian harvard

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Why is the sum of integers equal to -1/12

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Older blog post: This text is a loose continuation of the 2007 essay on Zeta function regularization Dear perplexed, there are many ways to see that your result is the right one. What does it mean the right one?

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Research related to "production of Knowledge" 

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Research related to "production of Knowledge" 

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Definition of Knowledge: the facts and the information created by usage of many other AOK.
/ the fact or condition of knowing something with familiarity gained through experience or association

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role of imagination in production of knowledge.

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role of imagination in production of knowledge.