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JTB model, Edmund Gettier, and Michael Clark's analysis of knowledge

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JTB model, Edmund Gettier, and Michael Clark's analysis of knowledge
In less than two and a half pages, Edmund Gettier completely shatters the analysis of knowledge held for hundreds of years by epistemologists through counterexamples displaying that a belief can be true and justified, but not constitute as knowledge. Michael Clark attempts to fix these problems presented by Gettier by adding another condition, in which a proposition would not only have to be a belief that’s true and justified, but also be fully grounded. In what follows, I will argue that Michael Clark’s analysis does not assist in solving the Gettier problem.
The objective of an analysis of knowledge is to state the conditions that are individually necessary and jointly sufficient for knowing a proposition. Necessary and sufficient conditions relate to conditional statements, which can be seen in the form: If X, then Y. There are four different ways in which necessary and sufficient conditions can be interpreted in an argument. 1) X might be necessary, but not sufficient for Y, 2) X is sufficient but not necessary for Y, 3) Neither are necessary, nor sufficient, 4) Both are necessary and sufficient. Given the statement: I live in Austin, therefor I live in Texas; in this case, living in Austin is sufficient but not a necessary condition for me to live in Texas, because I could live in any other city in-state and I would still live in Texas. However, if we flip it around: I live in Texas, therefor I live in Austin; it would follow that living in Texas is necessary but not a sufficient condition for me to live in Austin. From this, it can be said that an argument is valid if and only if it isn’t possible for the premises of an argument to be true without the conclusion being true.
Many attempts have been made throughout the years in order to understand what knowledge truly is. The concept of knowing a proposition is still a matter that is highly controversial and although there are many different models, the traditional and most widely accepted model used is the

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