In the beginning of Thucydides’ History, the Spartan King Archidamus offers an explanation of courage that emphasizes shame and self-control (see pp. 25-28 of the Woodruff translation, i.e. sections 1.80-85). First, analyze Archidamus’ conception of courage, by explaining the relation of his conception of courage to other Spartan ideals that Archidamus discusses, such as shame, self-control, good judgment, and moderation. Then compare and contrast Archidamus’ ideals with the ideals embodied in Socrates’ education of the future guardians in Republic Books 2-3, with specific attention to Socrates’ desire to cultivate self-control, a proper sense of shame, and moderation in his guardians. Do the citizens produced by Socratic education, as described in Books 2-3 of the Republic, seem likely to resemble the idealized Spartans described by King Archidamus? If so, then specify why and in which ways; if not, then explain why not. Be sure to support your views with specific examples and quotations from the texts.
Both Spartan and Athenian society emphasized courage as an important tenet. In Thucydides’ work, On Justice, Power, and Human Nature, Archidamus’ conception of courage is not founded on rash, unfaltering action but rather is based on calculating decisions, prioritizing long-term goals over instant gratification. On the other hand, Socrates’ notion of courage as explained in Plato’s Republic prioritizes lack of fear over any other value in relation to courage. The main difference between the Athenian and Spartan educational approach is Spartan decision making is driven from a place of fear whereas Athenian action is rushed and based in fearlessness; however, both societies value a holistic education for all to prepare citizens to lead honorable lives. First, Archidamus outlines the importance of good judgment, moderation, self-control, and shame and their connections to courage as key components of promoting prudent action. In Archidamus’ war speech, the Spartan king outlines the importance of good judgment in military strategy and adherence to law. Archidamus explains the importance of not rushing into war as, “ordinary people succumb, that war is safe and good” (Thucydides 25). Because of Archidamus’ experience, he pleads with the Spartans to not allow the excitement of war encourage rash decisions. This is an expression of great forethought, not a lack of courage as some critics may propose. Further, moderation is expressed as an important prong of courage regarding military strategy as courage does not justify unwarranted punishment of the enemy but rather careful and diplomatic deliberation. Archidamus advocates the Spartans ought not pillage the Athenians to the point where they are in such dire straits they can no longer be productive: “You ought to spare Athenian farmland as long as possible, and not make them so desperate that they are harder to control” (Thucydides 27). Thus, courage prioritizes long-term solutions over short-term gratification: when supplemented with mercy, courage is superior because it demonstrates that one is confident enough to not be concerned about enemy advances. Without moderation, one cannot be courageous as one cannot evaluate a given situation holistically. In a similar light, self-control creates an environment for controlled courage not simply based on utilizing brute force but also allowing for pragmatic limits to be drawn (Thucydides 27). Even though it may be less gratifying in the moment, this approach is preferable as a long-term strategy to defeat the Athenians. Archidamus believes that giving the Athenians time to negotiate on fair terms is not a sign of weakness; rather, it demonstrates Spartan confidence in their power over the Athenians. He states, “Do not take up arms just yet. Send to them instead, and make demands” (Thucydides 26). Simply being willing to fight in the face of danger is not courage. Rather, it is equally important to have self-control to know when it is appropriate to fight and when it is preferable to negotiate. Archidamus highlights the importance of giving Athenians time to concede to demands while covertly preparing for war to attack from a place of strength later. Additionally, shame and courage are closely linked in Archidamus’ understanding of war. The Spartans “are good soldiers because [...] self-control is the chief cause of a sense of shame, and shame of courage” (Thucydides 27). Archidamus emphasizes those who have shame will have courage as they do not want to be perceived as cowards, leading to self-control of soldiers. Archidamus admits “we are slow and make delays” but he also emphasizes that the Spartans should not “be ashamed” (Thucydides 27). Slowness of action is a manifestation of prudence and forethought and is linked to courage as the Spartans are not avoiding a challenge but are evaluating their options pragmatically. Through Socrates, Plato shows that courageous individuals remain steady regardless of the world around them: “the most courageous and most rational soul is least disturbed or altered by any outside affection” (Rep.2.381a). Even though Plato’s and Thucydides’ understandings of courage are rooted in maintenance of honor and dignity, the expression of these ideals in Spartan and Athenian societies is significantly different. The Spartan understanding of courage is driven by outside pressure as Archidamus specifically states that soldiers must be courageous to avoid appearing cowardly in contrast to Athenian belief (Thucydides 27). Thus, the Spartan understanding of courage is based much more on the perception of others and less on the virtue of courage itself. Furthermore, Socrates’ courage as seen in the guardians is rooted in lack of fear while Archidamus explains courage as rooted in slowness of action as a reaction to fear. When Socrates outlines the importance of children’s upbringing in Athenian society, he speaks of the need for making “them least afraid of death” (Rep.3.386b). Socrates presents his reasoning through a question: “Or do you think that anyone ever becomes courageous if he’s possessed by this fear?” (Rep.3.386a-b). Socrates believes that if individuals are raised to be unafraid of death, they will fight to the death for their city. On the other hand, Archidamus is concerned with preventing negative consequences of war: “Unprepared as we are, where could we get the confidence to rush into war?” (Thucydides 25). Even though Archidamus does encourage Spartan soldiers to act courageously, he does so from a place of fear of inferiority and Athenian power. On the other hand, Plato emphasizes having no fear when entering into battle as a preferable characteristic among citizens. Despite differences in expression of courage, Socratic-educated citizens have similarities to those described by Thucydides. Socrates believes individuals ought to appreciate the good and “sense [...] acutely when something has been omitted [...] and when it hasn’t been finely crafted or finely made by nature” (Rep.3.401e). He also believes individuals ought to internalize music and poetry as “rhythm and harmony permeate the [...] soul,” thus forming well-rounded citizens (Rep.3.401d). Archidamus explains how Spartans also prioritize an appreciation of the good with regards to military strategy: “Now I am not asking you to be so blind to the damage Athens is doing to your allies that you let them get away with it and do nothing to arrest them in their schemes” (Thucydides 26). Thus, Archidamus highlights the importance of understanding the totality of a situation, one’s strengths and weaknesses. Both authors thus prioritize the holistic individual but in different circumstances as Spartan culture places a greater emphasis on militaristic behavior. It is apparent that Athenian and Spartan approaches to courage have advantages and drawbacks. Examining both societies can aid the modern era in understanding the best mode for civic engagement. It is important to realize there is a time and a place for the Athenian approach to courage and the Spartan method to this virtue. Careful deliberation in modern politics, especially in instances of foreign intervention, is essential. At the same time, leaders of states must be able to make decisive judgments and lead their countries accordingly. With this approach to politics and international relations, countries will be able to foster stable alliances and find themselves in a place of power in global affairs.
If the integral from 1 to k of (dx/(x*sqrt(x^5-1))) equals the integral from k to infinity of (dx/(x*sqrt(x^5-1))), find the value of k.
This problem is relatively straightforward once you solve for the indefinite integral. You will need to use system of equations and u-substitution for this problem. First, let u = (x^5-2)^1/2; du = 5x^4/(2(x^5-2)^1/2)dx Thus, the new form of the integral becomes the integral of (2(x^5-1)^1/2/5x^4(x^5-1)^1/2) = 2/5*integral of (1/x^5) = 2/5*integral of (1/(u^2+1)) =2/5 arctan(u) =2/5arctan(sqrt(x^5-1)) + C From there, you just solve for system of equations to arrive at a numerical answer. The hard part is solving for the integral!
Compare Machiavelli's understanding of virtù as explained in The Prince in comparison to Aristotle's understanding of virtue and concern for the human good.
The main difference to be found between Machiavelli's and Aristotle's understanding of virtue derives from the key assumptions about how the authors believe society ought to be structured. Machiavelli's understanding of virtue aligns with his view that the many are simply tools for the ruling class, or the prince, to manipulate to further their own power. With this mentality, Machiavelli realizes that life is far from ideal and it is necessary to realize that there are instances in which utilizing vices may guarantee the safety and security of power while virtue may at times lead to one's demise. Further, Machiavelli sees virtue as a way to manipulate the many into submission. For example, Machiavelli advocates that one ought to appear Christian in values towards his subjects but not actually practice Christian virtues as they are not practical for the maintenance and acquisition of power. With this, it is clear that Machiavelli does not believe that there is an objective good or effectual truth -- one must take actions to further one's power. However, Aristotle believes in this notion of the "objective good" and believes that each citizen's end is to promote goodness and the best quality of life within the city. Aristotle holds virtue as he explains in Politics in such high regard that he believes that the virtue of the individual is more important than law. He explains laws are only guidelines and cannot prevent crime -- even if a law exists, a citizen can still break it. Thus, Aristotle argues that citizens should obey laws because of their desire to promote inner goodness and a violation of a law is net detrimental to society. In a similar light, Aristotle argues that laws should not be obeyed out of fear of punishment but out of the desire to promote the common good within society. When evaluating Machiavelli and Aristotle, it is imperative to realize that their different understandings of virtue may not necessarily be tied to their own moral standings of the realization of virtue but is actually a result of their understandings of society. Aristotle believes that the only way to establish true political order is to create a basis of goodness within political life and society whereas Machiavelli sees society as an opportunity for the elite to grab for the augmentation of their power. With this, Machiavelli sees virtue as a tool whereas Aristotle sees virtue as a foundation for modern political life.