Epistemological Relativism (ER) is Self-Refuting
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1) It is often said that Protagoras’s epistemological relativism (ER) is self-refuting. Explicate ER, and then state and evaluate the Socratic argument that ER is self-refuting. Hint: It would then be appropriate to discuss the Justified True Belief (JTB) analysis of S knows that p, as an alternative to ER.
2) Discuss the three theses of Gorgas’s nihilism, as reported by Sextus Empiricus. Demonstrate that the first (metaphysical) thesis is self-refuting. It will be helpful for the task of refuting Gorgias's nihilism to discuss and apply the JTB Justified True Belief (JTB) analysis of S knows that p. What surprising metaphysical result(s) follow(s) from the self-refutation of Gorgias’s first thesis?
Textbook: The Great Conversation: A Historical Introduction to Philosophy
by Norman Melchert and David R. Morrow (8th edition)
Extra reading:
The Four Corollaries of Melissos
According to Sextus Empiricus, and lightly revised by your instructor.
The Goddess reveals to Parmenides: Being is. Non-Being is not.
1) It is permanent and unchangeable.
[The Parmenides conjecture]
2) (Therefore) It is uncreated [from 1]
3) (Therefore) It is whole, indivisible, and everywhere continuous.
[from 1]
4) (Therefore) It is identical with the thought that recognizes it.
[from 1, 3]
ZENO'S HIDDEN PREMISES EXPOSED!
To continue our discussion of the dichotomy paradox, we wlll need to define the following term:
Supertask = df
Any series S of sequentially performed routine procedures (Call these procedures: the sub-routines of S.) such that there is no last member of S.
1) The Euclidean Assumption = df
There is a one-to-one mapping (called by mathematicians a bijection) of the points of space and the instants of time with the real number axis (the Continuum).
Another way to express this assumption is to affirm that space and time are both continua, or in modern relativity physics, spacetime is a continuum.) You can intuitively capture the idea of a continuum as follows: For any pair of numbers, or spatial points, or instants of time, there is a third number, or spatial point, or instant of time, that lies between the respective members of the initial pairs.
I need this done before 11:59 25, January please
2) Let S1 = { 1/2 + 1/4 + 1/8 + 1/16 + . . . }.
An infinite series (such as S1) sums to infinity.
3) Achilles's attempted traversal of line segment AB constitutes a supertask.
4) As the sub-routines of a supertask have no last member, it is impossible that a supertask can be completed within any finite temporal duration.
Subject and Section
Professor’s Name
January 26, 2023
Philosophy Discussion
1.
Protagoras's epistemological relativism (ER) holds that knowledge is relative to the individual; what is valid for one person may not be true for another. In other words, there is no objective truth, and knowledge is subjective.
The Socratic argument that ER is self-refuting states that if ER is true, it is only true for the person who holds it. However, if it is only true for that person, then it is not true for anyone else, including the person who holds it. Therefore, ER cannot be true for anyone, including the person who holds it and is therefore self-refuting.
An alternative to ER is the Justified True Belief (JTB) analysis of knowledge. According to JTB, to know something is true, one must have a true belief, justified by evidence and believed by the person. In this way, JTB allows for objective truth and knowledge rather than the subjectivity of ER.
It is important to note that the self-refutation argument needs to be more conclusive and that the debate between epistemological relativism and the JTB analysis of knowledge is ongoing.
2.
Gorgias's nihilism, as reported by Sextus Empiricus, is a philosophical position that consists of three theses:
The first thesis is a metaphysical one, which states that nothing exists.
The second thesis is ethical, which states that even if something exists, we cannot know anything about it.
The third thesis is evaluative, which states that even if we could know something about something that exists, it would not be worth knowing.
The first thesis that nothing exists is self-refuting because to make the claim that nothing exists, Gorgias must exist, and there must be something (i.e., a statement) that can be said to be false. In other words, for the statement "nothing exists" to be meaningful, there must exist the person who is making the statement and the statement itself, which means that something must exist.
The JTB analysis can be applied to this thesis by considering the criteria that must be met for Gorgias to know that nothing exists. According to JTB, for Gorgias to know that nothing exists, his belief must be true, justified by evidence, and believed by him. However, since the belief that nothing exists is self-refuting, it cannot be true. Therefore, Gorgias cannot know that nothing exists.
The self-refutation of the first thesis of Gorgias's nihilism leads to the surprising metaphysical result that something must exist. This means that his nihilism is not coherent and can't be accepted as...