In this week’s reading of What is this thing called Knowledge by Pritchard discusses how people define knowledge. According to Pritchard, everyone has difficulty in defining knowledge, with this difficulty also known as the problem of the criterion. He argues that the person needs to identify instances of knowledge in order to determine the criteria for knowledge (21). This problem leads to the Justified True Belief Account (JTB), which proves that a person has knowledge of something if he has a proof for it, or justification for his belief. Let’s look at an example for better clarification.

Jong is told by Joe that someone in his class has a pencil (a). Jong believes Matt has a pencil, because Matt is holding an object that looks like a pencil (b). Therefore, Jong believes that someone in his class has a pencil (c).

In this example, Jong is justified in believing that someone in his class has a pencil, simply because he saw Matt holding one. Since Jong has a proof in his belief, it is considered as JTB. However, Gettier argues that it is possible for a belief to be true and justified without being knowledge, because two features constructs Gettier’s cases: fallibility and luck. In his examples with two cases, he argues that “the combination of truth, belief, and justification does not entail the presence of knowledge” (Hetherington).

As an example for Gettier’s arugment, what if Matt was actually holding a pen that looked like a pencil? This statement totally contradicts Jong’s belief. However, if a student other than Matt happened to have a pencil, then it is out of pure luck that Jong’s belief is, in fact, true and justified. However going with Gettier’s argument, this cannot be considered as “knowledge” because it was out of luck that Jong’s JTB was in fact true.

In another class reading by Feldman, Meyers and Stern argued that if the principle (ex. Jong’s belief) is false, then the counter-example that Gettier gave fail. They argued that (a) can justify (c) only if (c) is true (Feldman 68). However, Feldman disagrees (defending Gettier), saying that “there are examples that do not rely on this false principle” (Feldman 68).

To fully understand what Feldman is saying, let’s go back to the example. Let’s say that Matt is not holding a pencil, but a pen that looks like one. For this example, Meyers and Stern would say Jong’s JTB in (c) is false because the principle is false. However, what if Jong generalizes a statement that he deduced from (a)?

Someone in Jong’s class told him that someone in Jong’s class has a pencil, and that person is very good friend of Jong, who he trusts (d).

In this generalization, we can say that from (d), Jong believes (c). As a result, Jong has a JTB in (c) because of this proof, even though Jong still doesn’t know (c) (Feldman 69).

An outside source was found to see the arguments that went against the Gettier’s cases. Hetherington proposed a contrary interpretation of luck, as he calls this interpretation the Knowing Luckily Proposal (Hetherington). He gives an example by reinstating Gettier’s Case I. Hetherington states that Smith is lucky to have a belief that whoever gets the job will have ten coins in the person’s pocket (which happened to be true). This does not mean that Smith is lacking knowledge, but rather came close to lacking knowledge (Hetherington). So he concludes that “because Smith would only luckily have that justified true belief, he would only luckily have that knowledge.” (Hetherington). I found this interesting because this proposal directly goes against Gettier’s reason for refuting the JTB Account.

I wonder now: will we ever be able to clearly define knowledge? With every proposed argument comes with a rebuttal. Maybe we will never have a unanimous agreement. Who knows what’s going to happen in the future?

Sources:

http://www.iep.utm.edu/gettier/ (by Hetherington)

How do we define Knowledge? This is a fundamental question that epistemologists debate and have formed numerous arguments towards. In Chapter 3, Pritchard suggest that the task to define knowledge is centered on the problem of criterion. The problem of criterion proposes two claims, the first being, “I can only identify instances of knowledge provided I already know what the criteria for knowledge are” (Pritchard 20). The second claim is “I can only know what the criteria for knowledge are provided I am already able to identify instances of knowledge” (Pritchard 21). As epistemologists, these claims give us two options. We can either assume we know the criteria for knowledge and use them to identify cases of knowledge (methodism), or we can assume that we can identify cases of knowledge and deduce the criteria for knowledge from similarities between these cases (particularism). These two methods counter each other and split epistemologists into separate beliefs about how to go about finding a definition for knowledge.

Although Pritchard stresses in Chapter 3 the importance of justification for one’s belief, he also states that matters are not that straightforward. This is due to the work of Edmund Gettier, who throws a wrench in the classical theory of knowledge. Pritchard presents us with an example where John reads the correct time from a stopped clock. In the case, John meets the conditions for the classical theory of knowledge; however, John’s JTB is based on luck. Gettier therefore argues that there is a fault in the JTB definition of knowledge due to the fact that luck can sometimes still sneak in. According to Gettier, John would not have knowledge.

Naturally, Gettier’s counter-examples to the classical theory of knowledge caused uproar in the philosophy/epistemology community. In response, epistemologists have attempted to narrow the gap between JTB and knowledge, “… a natural idea is to amend one’s analysis of knowledge by including an explicit ‘anti-luck’ condition” (Ichikawa). One major concern is the factor of presuppositions in Gettier’s work. Can we say that you have knowledge if one has a justified true belief and none of the presuppositions are false? Pritchard explains, “… it is difficult to spell out this idea of a presupposition such that it is strong enough to deal with Gettier cases and yet not so strong that it prevents us from having most of the knowledge what we think we have” (26).  The complex question of what defines as a presupposition is raised. D. M. Armstrong argues that, “Gettier’s examples are defective because they rely on the false principle that false propositions can justify one’s belief in other propositions” (Feldman 68). Between these opposing beliefs, there is a middle ground where we must have an understanding of presuppositions so that Gettier cases hold, yet non-Gettier cases are not affected by this understanding.

So have we found a method yet that will help us arrive at a definition for knowledge? For every theory of how to begin defining knowledge that has been presented to us thus far, we have been given counter-examples. Pritchard presents us with methodism and particularism and Gettier finds problems with the JTB account of knowledge that Feldman then goes on to counter. Feldman writes, “If his evidence is true, or only if he knows it to be true, there are still counter-examples to the justified true belief analysis of knowledge of the Gettier sort” (69). As Pritchard concludes at the end of this chapter, we do not have a clear method that gives us a generally acknowledged unambiguous definition for knowledge.  The question is, with so many opposing methods and counter-examples, will we ever?

Outside Source: Ichikawa, Jonathan Jenkins and Steup, Matthias, “The Analysis of Knowledge”, The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/spr2014/entries/knowledge-analysis/>.

The challenge of defining knowledge has been plaguing epistemologists and philosophers since the origins of epistemology. There are two methods of classification for the definition of knowledge, methodism and particularism. Pritchard states that most epistemologists “have followed Chisholm in opting for particularism instead” (Pritchard 22).  Particularism is much more sensible than Methodism as it is much easier to produce a criteria for knowledge once you have identified a particular instance of knowledge.

Until 1963, the tripartite definition of knowledge had been relatively unquestioned and accepted as the definition of knowledge. That is until the tremendous epistemological impact of Edmund Gettier’s work. If the Gettier case presents a consistent counter-example to the JTB account of knowledge, then the JTB account of knowledge is not a valid definition of knowledge. Almost all epistemologists agree that Gettier disproved the justified true-belief conception of knowledge (Hetherington). According to Gettier, one could have a justified true belief and yet still lack knowledge as one can get lucky (Pritchard 23). The easiest example to understanding the Gettier case is case one about Smith and Jones. Gettier’s conclusion, “It is not the case that if S believes that P, is justified in believing that P and P is true, then S knows that P” is very easy to understand (Gettier). Due to the fact there is no universally accepted definition for knowledge, epistemologists will keep debating which definition they support.

The outside source I used talked about epistemologists use of Safety+.  Safety + states that a truly belief is safely formed “given how it has been formed and given the surrounding circumstances in which it has been formed, it would have only been formed if true (Hetherington). Although there is much debate on the concept of Safety +, the concept of Safety + generally supports the Gettier case. This is due to the fact that Smith had not formed his belief as true due to the fact that he overlooked facts that would have made the belief true (Hetherington). As previously stated, due to the fact that the Gettier example lacks safety, it cannot truly be defined as knowledge.

The counter arguments to the Gettier cases criticize the fact that the cases rely on the false principal that false propositions can justify one’s belief in other false propositions (Feldman). Those who argue against Gettier’s examples say that a proposition can only justify another proposition if it is true (Feldman). If more epistemologists were to agree with views like Feldman, the JTB account for knowledge would become the most accepted view. Defining knowledge becomes an almost impossible task, as the definition of what knowledge truly is, is rather subjective. This is because arguments can be made for any definition of knowledge.

I agree with the conclusion Pritchard ends the chapter with. I do not think that there will ever be a widely accepted definition of knowledge due to the abundance of counter examples to theories, and because knowledge of what knowledge is almost impossible to ascertain. Will knowledge ever have a perfect dictionary definition? Not in the sense in which epistemologists desire.

Sources:

Hetherington, Stephen “Internet Encyclopedia of Philosophy.” Knowledge []. N.p., n.d. Web. 15 Sept. 2014.

Chapter three in Pritchard is titled “Defining Knowledge,” yet much of the chapter presents   different, conflicting ideas of what knowledge is. The reason that the definition of knowledge is seemingly impossible to agree upon among epistemologists and philosophers is known as the problem of the criterion. This problem is summarized by Pritchard as, “I can only identify instances of knowledge provided I already know what the criteria for knowledge are,” and, “I can only know what the criteria for knowledge are provided I already am able to identify instances of knowledge” (20-21). This is a Catch-22 of sorts because the claims make both finding criteria for knowledge and identifying instances of knowledge necessary to determine the other. This in itself raises the question if defining knowledge is a legitimate effort at all.

Instead of accepting that knowledge cannot be defined, philosophers have attempted to come up with other working definitions, such as knowledge as Justified True Belief, which is known as the classical account of knowledge. However, this theory hasn’t satisfied the need for a definition as it has “been shown to be completely untenable” (Pritchard 23) by Edmund Gettier. Gettier uses cases, such as John’s Justified True Belief that it’s 8:20am, to prove that one can have Justified True Belief and still not have knowledge. John is justified in his belief that it is 8:20am because his trustworthy clock reflects that time and he comes downstairs at that time every morning. The belief is also true, but he does not have knowledge because he is unaware that his clock happened to have broken at 8:20am the day before.

After deconstructing one of Gettier’s arguments in class, we found that he posed a sound argument. Yet, Feldman tells us that some philosophers such as D.M. Armstrong find fault in Gettier’s argument in that, “Gettier’s examples are defective because they rely on the false principle that false propositions can justify one’s belief in other propositions” (68). Feldman goes on, however, to reject the claim that Gettier’s examples are defective by creating a case in which the proposition that causes one to be justified in their belief is a true proposition, but that person still lacks the knowledge.

So we are faced with Gettier’s argument, Armstrong and others’ counter argument, and Feldman’s counter argument to the counter argument. What this tells me is that there are and have been talented philosophers and epistemologists who disagree about the definition of knowledge and perhaps will never agree on its definition. This brings me back to the problem of criterion. Immediately, I thought that the only solution to the problem of criterion would be that the criteria for knowledge and instances of knowledge are the same thing. Is it possible that an instance of knowledge might BE knowing the criteria for knowledge, and that neither precede the other, but happen at the same time? Perhaps that means that knowledge is self-defined, and each person’s instance of knowledge is knowing their own criteria for knowledge. For example, a scientist knows his criteria for knowledge is that it must be experimentally proved. This is both an instance of knowledge and criteria for knowledge. Do you believe that there is just one definition of knowledge? Is knowledge self-defined?

In this week’s reading, Feldman presents an interesting point from D.M. Armstrong. Armstrong states that possession of the “grounds” necessary for the JTB Account are in fact “too weak to serve as suitable grounds” for knowledge (Feldman 68). In other words, regardless of the truth or falsity of the “justifiably believed grounds” that prove a true belief, those grounds are not means to posses knowledge (Feldman 68). Feldman disagrees with this statement and concludes, “there are examples very much like Gettier’s that do not rely on this allegedly false principle” (Fedlman 68). Here, meaning that these other examples do not rely on the defects of Gettier’s argument, yet succeed in the way Gettier’s argument does when discounting the JTB Account.

In our reading in Pritchard, we are given two examples, one with Sally and one with John. In John’s example, he lacks knowledge because his false belief that he is looking at a working clock is considered to be a presupposition of his belief in time. In Sally’s example, she is not deprived of knowledge because her false belief that the clock is regularly maintained is not a presupposition; because she is looking at working clock (Pritchard 27).

These examples together are meant to criticize the reliability of Gettier’s argument, but the result is not enough to make his argument completely wrong. Can we ever find a way to completely criticize this reliability? Gettier’s argument is not completely discounted yet it is not completely bulletproof either (based on what was said about presupposition in Pritchard). Despite this dilemma, what we need to take away from Gettier is “that you need to demand more from the world than simply that one’s justified belief is true if you are to have knowledge” (Pritchard 27).

Furthermore, we discussed in class how the JTB Account was wrong as criticized most famously by Gettier. There are then also those who believe Gettier is wrong. What we see is a succession of “right and then proved wrong” arguments. Will we ever find an answer to how we obtain knowledge and how we can know what constitutes this obtaining of knowledge? I did a little outside research on this. In an article I read in Philosophy News, the author gives us a sort of chronological panorama of the evolution of knowledge. One idea, which is briefly mentioned in Pritchard is the idea of skepticism or “postmodern epistemology.” Basically, postmodern epistemologists, “reject the idea that we can ever be fully justified in holding that our beliefs line up with the way the world actually is. We can’t know that we know” (Pardi).

I think that, based on what we have learned so far, defining “knowledge” goes two ways. One way is that we accept that we will never know exactly how we know or what it means to know what knowledge is, but we can get as close as possible by countering what those before us have discovered. The other way, is that we will never know that we know because we cannot step outside ourselves and our own beliefs – which then brings us back to the criterion: if one doesn’t already know what knowledge is and what the criteria of knowledge are one cannot identify instances of knowledge and vice versa. Up to this point, every argument has had a criticism; all we know is that we can merely speculate how it is we come to know something, and even then do we really know that? What does knowing itself entail? Will we ever know? I wish I had answers to these age-old questions but my conclusion is simply that what we take to be knowledge is determined by our perspective on the world and how it is determined.

Outside source: Pardi, Paul. “What Is Knowledge?” Philosophy News. N.p., 22 Sept. 2011. Web. 14 Sept. 2014. <http://www.philosophynews.com/post/2011/09/22/What-is-Knowledge.aspx>.

The Classical Account of Knowledge, where knowledge is understood as a justified true belief was discussed in this week’s reading of Pritchard. In attempt to define knowledge, we must be able to see it from multiple aspects. So we consider the aspect where knowledge as a justified true belief. “Knowledge is to be understood as justified true belief, where a justification for one’s belief consists of good reasons for thinking that the belief in question is true” (Pritchard 28). This leads us to the JTB Account for Knowledge, which is an analysis that claims that justified true belief is necessary and sufficient for knowledge. Now if we accept this analysis of knowledge to be true, that raises even more concerns. What is truth? What is a proper justification for that truth? That is when Gettier comes along with an article that shows that the JTB Account for Knowledge may be false. With the use of logic, Gettier successfully proves that the consequent (P is true, S believes that P, and S is justified in believing P), is not jointly sufficient of the antecedent (if and only if S knows that P). “I shall argue that [the JTB Account of Knowledge] is false in that the conditions stated therein do not constitute a sufficient condition for the truth of the proposition that S knows that P” (Gettier 345). Basically, he proved that one could have a justified, true belief and still lack the knowledge of one’s belief because that belief could have been obtained through luck (Pritchard 23).

On the other hand, there is another philosopher, Richard Feldman, who published an article, An Alleged Defect in Gettier Counter-Examples, that essentially describes how Gettier’s work was flawed: “I conclude that even if a proposition can be justified for a person only if his evidence is true, or only if he knows it to be true, there are still counter-examples to the justified true belief analysis of knowledge of the Gettier sort” (Feldman 69). He came to this conclusion with the help of many other researchers, in which Feldman too, agrees to conclude that Gettier came up with his conclusion using false evidence.

This all leads back to the big question: How does one begin to define knowledge? It is evident that this comes with great difficulty, also known as the problem of the criterion. This basically means that one is only able to identify circumstances of knowledge only if one knows the criteria for what knowledge is and one can only know what the criteria for knowledge is as long as one is able to identify specifics of that knowledge? Well, one can start by finding the common variable in all cases and then become able to ascertain what knowledge really is.  But in the end, it can be concluded that one needs to understand knowledge in an entirely new way, where one cannot just simply believe in the truth of a question (Pritchard 29).

Other than the readings, I referred to:

Ichikawa, Jonathan and Steup, Matthias (2012) ‘The Analysis of Knowledge,’ Stanford Encyclopedia of   Philosophy, < http://plato.stanford.edu/entries/knowledge-anaylsis/>.

The complex dilemma that we have to face from the readings is essentially how to define knowledge and differentiate it from true belief.

After completing the readings, I was eager to claim that someone can know something without having full knowledge of it. For example, while I know that (-b±√b²-4ac)/2a and that a²+b²=c², I do not have a full understanding of why these are true and accepted mathematical equations. I would have gone so far as to argue that I do not have knowledge of these. Certainly, I know how and when to use them, but by Pritchard’s standards in What Is This Thing Called Knowledge, I do not know why I use them and therefore lack knowledge on both the quadratic formula and Pythagorean’s Theorem. The evidence and reasoning that I needed to justify my true belief (which even then is not enough to be knowledge as noted by Edmund Gettier) stems merely from the fact that I learned these theorems in class and had practiced them enough to know that the answers I derived from such equations were true.

When does simply accepting something that we’ve learned in class become knowledge? Or does it ever?

Due to these questions, I decided to do some research and came across the terms “a priori knowledge” and “a posteriori knowledge.” A priori knowledge is independent from personal experience while a posteriori knowledge is developed from our personal experiences. These were fully discussed by Emmanuel Kant, a German philosopher, and he held that fields such as mathematics, physics, and metaphysics fall into this umbrella of knowledge. Therefore, the concepts that I have come to learn and accept in mathematics are examples of a priori knowledge, that I have gained independently and which are accepted universally.

Yet this makes me think of the Ptolemaic system (or geocentric model) which states that the Sun revolves around the earth. Of course, we now know this to be false due to the work of Nicolaus Copernicus. However, before his discovery, it was a system that was generally accepted in the Roman and medieval worlds. While we know it was a false belief, for those during ancient times, it was accepted and considered true. There are people who have long been dead who believed that the Earth was the center of the universe. This now transitions us into the topic of belief versus knowledge. Belief, even true belief (as discussed in the readings, particularly in The Meno by Plato) cannot be considered knowledge. Belief can simply give more credibility to knowledge that one has gained because one cannot truly purport to know something if they do not fully believe it. To know is, in a sense, to believe. But, conversely, it does not mean that to believe is to know.

Knowledge cannot be narrowed down so easily to “getting things right” because aside from the possibility of one merely being lucky (which was discussed by Pritchard and Gettier), there are many things that we as humans do not fully understand. For example, when we begin to approach questions that no one truly knows the answers to, such as whether or not there is a god or whether or not abortion is ethical or what is our purpose in life, we reach an area in which knowledge is difficult to determine. They may feel that they know and perhaps they may be right, but that does not necessarily mean that these beliefs are knowledge. When can (assuming they can) any of the answers that people develop to these questions cross the barrier of belief and transition into the knowledge we as humans naturally seek? Sure, we certainly have a slew of theories with plenty of evidence that would typically justify such theories as Plato suggests. But while we have evidence for theories such as evolution, that does not stop people from whole-heartedly believing in God and decrying the alleged falsity of such a theory. Will the answers that we develop for the questions that we have yet to find concrete evidence for remain beliefs forever? Until we find concrete evidence that “ties them down by (giving) an account of the reason why”, we can never gain knowledge on the answers to these questions (Plato, The Meno).

There was, I felt, an important line to note in the last section of the first chapter in What Is This Thing Called Knowledge: “whether or not the world is round, for example, has nothing to do with whether or not we think that it is, but simply depends upon the shape of the earth.” I know that we will discuss truth throughout the semester, but this begs the question of whether or not we can know if something is really true. We can be misled and deceived, we can be wrongly taught and filled with fallacies, accepting these lies as true. We can live a life devoid of truth if we so choose it or even if we do not choose it. How can we ever really know the truth if we are only taught lies?

From these readings, the only thing that I can firmly conclude is that I do not really know anything. None of us do.

Sources (other than the readings):

“a priori knowledge.” Encyclopaedia Britannica. Encyclopaedia Britannica Online Academic Edition. Encyclopædia Britannica Inc., 2014. Web. 08 Sep. 2014. <http://www.britannica.com/EBchecked/topic/117/a-priori-knowledge>.

The two opening chapters of What is This Thing Called Knowledge? by Duncan Pritchard address the following questions: What is knowledge? and Why should we care about it? These same general questions were asked by Simon Blackburn in his book, Think. In it’s introduction, Blackburn tells us that obtaining the answers to these inquiries is a matter of reflection since we don’t exactly know how to begin determining their conclusions (Blackburn 2). In order to have the type of knowledge in question, propositional knowledge, you are required to believe the appropriate proposition, which, in turn, must be true (Prithard 5). Therefore, we see that knowledge requires truth as well as belief. This leads us to an interesting point. Does believing/thinking something make it true? Pritchard argues that it doesn’t. When someone believes something, they believe it to be true, and it may or may not be. Once it is determined that said proposition is, in fact, true, we must decide if the person actually knew or was subject to a lucky guess. It could be the case that they did actually know it was true, and it was, but Prithard tells us that you cannot gain knowledge completely by chance (Pritchard 6). This means that making a guess at something and coincidentally being right does not mean you have actual knowledge of it. Let’s now look at the second question that was posed. Why should we care about knowledge (and true beliefs)? There are different  approaches to responding to this question. According to Pritchard, we are aided in achieving our goals in life by true beliefs. This is because it is useful, if not necessary, to possess knowledge that was applicable to these goals. Blackburn outlines the high, middle, and low-ground approaches as to why we should care about knowledge. The middle-ground is most likely to be accepted. It proposes that reflection is continuous with practice meaning that the way you do things is a result of how you thought about it which is why it matters. It even affects whether or not you do said thing at all (Blackburn 4). Reflecting on and thinking about the truth of things does not equate to knowledge on the subject. Pritchard contrasts and ranks the differences between true and false beliefs and actual knowledge. True beliefs are better than false ones, but knowledge is even better. Knowledge tends to be more concrete. It becomes ingrained, whereas true beliefs are unstable and subject to change (Pritchard 14). You may believe in something and find it isn’t as reliable as you thought, and lose that belief. On the other hand, if you know something for sure, it would be difficult to change how you think about it. As much sense as this makes, Plato argues the contrary in a way that is also justifiable. In Meno, he supports that if someone has no knowledge of something, but has a correct opinion, they can be equally as useful as someone possessing knowledge. This raises the question of the value of knowledge. Ultimately, knowledge is important because the man who has it will most definitely succeed, whereas the one with simply a right opinion may not (Plato 343-4).

Blackburn, Simon. Think: A Compelling Introduction to Philosophy. Oxford: Oxford UP, 1999. Print.

Plato, and R. S. Bluck. Meno. Cambridge: U, 1961. Print.

Pritchard, Duncan. What Is This Thing Called Knowledge? London: Routledge, 2006. Print.

What is Knowledge? The readings for this week give us a precise, however, complicated explanation. In What is This Thing Called Knowledge, chapter 1, knowledge is defined as a true belief. In order for one to truly have knowledge, one must believe a proposition, and that proposition must actually be true. For example, if one believes the sky is purple, when it is clearly not, that person does not have knowledge. In the book What is This Thing Called Knowledge, Pritchard makes it clear to distinguish propositional knowledge (e.g. knowing that 2+2 is 4 and Obama is the president) versus ability knowledge, which is the “know-how” (e.g. knowing how to ride a bike or swim). However, the more interesting question comes up later in the chapter and even in the Plato article. Does someone have knowledge if they only have a true opinion by accident or by luck? If someone guesses that 15+15=30, and they so happen to be right, would their true opinion be actual knowledge? I suppose that the first opinion is most definitely not knowledge, but I do believe that in certain circumstances, such as the one listed above, the person will now gain knowledge from their true opinion by gaining evidence for it. Similar to the Plato article, where it states that true opinions are good if they are kept, but until they are tied down with actual evidence and reason, they cannot be knowledge (Plato 344). I agree with this statement whole heartedly that if someone gains evidence then they will have knowledge, but how can we tell if that person is gaining evidence and reason on why their belief is true? In simple examples like the 15+15=30, would the person need more evidence or practice before Socrates and Meno conclude that person knows the answer? In the chapter we read, Pritchard thinks that because the person has just guessed or just “merely got it right.” they will only get the question right some of the time, not all of the time like someone with actual knowledge would have. Basically anyone can believe something is true and there be a match with what is the case and our belief, or just getting it right, but there is more to knowledge than that (Pritchard 5). He states, “…To say that someone has knowledge is to credit that person with a certain kind of success [i.e actually believing a true proposition]” (Pritchard 5). He gives multiple examples of someone betting on a lucky horse just because of the name, and that horse surprisingly winning at the end and an archer versus someone who is not. In the horse example, I would agree that the latter may not have actual knowledge in betting or on the stats of the horses to make an intelligent bet only because he basing his true belief on luck or irrelevant factors—and in this case, the results are variable. With this example compared to the math example, it seems as though choosing luck every time will not make one knowledgeable, but if the person in the math example continues to make the true belief that 15+15=30 then eventually that person would have enough evidence, it seems, to have that as knowledge (no guessing required). Just as both articles stated, knowledge must be credited solely to the person and not to luck or by accident. I believe in this statement, however, I do believe that in simple examples like the math one I gave knowledge can be tricky to determine. When do you count that person’s answer as knowledge? Where do you draw the line where someone is just guessing and where someone finally learns and gets it right? Where does learning come into play in the question of knowledge—if it even has a place? And if learning doesn’t come into play then how do we really know anything and gain knowledge, or is it just something we have in a certain aspect or we don’t?