Symbolic Logic: Conditional/Indirect Proofs and Proving Theorems

Hey guys! So, this time, we’re going look at other methods we can use to construct proofs when just deriving from the premises isn’t enough.

Conditional Proof (CP)

The setup:

Basically, you use this method when the conclusion or a part of the conclusion you want is a conditional. This makes it so you assume the predicate in order to derive the consequent. Here’s an example:

Indirect Proof (IP)

The setup:

For this method, you use this primarily when the conclusion is a negated statement. You assume the un-negated form of the conclusion and attempt to find a contradiction so that the assumption is false, thus ending at the negated form. It also works the other way around where the conclusion isn’t negated so you make the assumption negated instead and then use the DN rule at the end. It’s also super useful when proving theorems where you have a limited plan of action. An example:

Theorems

Theorems are formulas that can be proven true without premises so the proofs for theorems have the additional challenge of not being able to build off of premises. Therefore, the above two methods are essential to be able to do proofs of theorems. Here’s an example:

RULES

  1. All assumptions must be discharged(closed).
  2. Lines between different assumptions must not cross.
  3. Once discharged, steps within the subproof cannot be used anymore.

On to the next page for a few practice problems!

Symbolic Logic: 10 Replacement Rules

This is part two of our little intro to Symbolic Logic. We’re going to expand our repertoire of rules we can employ in our proofs. These rules are all about putting logic statements into an alternative form. A lot of these rules will be familiar as they’re used in mathematics. One of the differences between these rules and the basic 8 is that these are reversible, hence the :: symbol to denote a two-way operation. The format of this post is going to be similar to the last one; the rules will be listed first, then some simple examples and then a couple of practice problems on the following pages.

1. Double Negation (D.N)

p :: ~~p

2. Commutation (Comm.)

p V q :: q V p

p • q :: q • p

3. Association (Assoc.)

[(p V (q V r)] :: [(p V q) V r)]

*applies to AND operators the same way*

4. Duplication (Dup.)

p :: p V p

5. DeMorgan’s Law (DeM.)

~(p V q) :: ~p • ~q

This law describes how a negation gets distributed into a parenthesised statement. It negates the two variables and switches the operator from an AND to an OR or vice versa. It only works on AND and OR operators though so if you have a (BI)CONDITIONAL operator inside the parenthesis, you’ll need to use one of the later replacement rules to make them into one.

6. Biconditional Exchange (B.E.)

(p ≡ q) :: [(p ⊃ q) • (q ⊃ p)]

7. Contraposition (Contra.)

(p ⊃ q) :: (~q ⊃ ~p)

8. Conditional Exchange (C.E.)

p ⊃ q :: (~p V q)

9. Exportation (Exp.)

[(p • q) ⊃ r] :: [(p ⊃ (q ⊃ r)]

10. Distribution (Dist.)

[p • (q V r)] :: (p • q) V (p • r)

[p V (q • r)] :: (p V q) • (p V r)


Examples




Alright y’all, on to the practice problems.

Symbolic Logic: 8 Basic Inference Rules

Hi y’all! So, if you’re computer science majors/philosophy major/etc., you probably have to take this class in college. I love this stuff because it’s very procedural and the proofs they give for you to solve are like puzzles and puzzles are super fun. Today, we’re gonna look at the 8 basic rules and then we’ll look at the replacement rules and more. I’m going to assume that y’all know the basic structure of sentential logic including operators and truth tables. Let’s get started.

Structure

A proof is a procedure which is supposed to derive the desired conclusion from a set of premises. To do this, the proof has to be set up in a certain way. First, all lines of a proof must be numbered. The premises make up the first lines of the proof along with the desired conclusion. Then, all subsequent derivations from the premises are listed below with the justification for each step listed along the right side, noting which rule was used and what lines of the proof were referenced. Here’s an example:

  1. Premise Pr. (for premise)
  2. Premise Pr. /:. Conclusion
  3. Derivation (Name of Rule) 1, 2 (lines 1 & 2 referenced)

For our purposes on this page, the visualisations for each of the rules below will not be written in this vertical fashion as they are cumbersome to format in the WordPress editor so it’ll be horizontal.

Let’s get into the rules and then work on some examples which will be on page 2.

1. Simplification (Simp.)

p • q /:. p

OR

p • q /:. q

If there is a conjunction, then both conjuncts can be individually represented as being true by themselves.

2. Conjunction (Conj.)

p; q /:. p • q

If two variables are true, then they can be joined in a conjunction.

3. Addition (Add.)

p /:. p V q

This rule is incredibly powerful as it allows you to introduce new elements into a disjunction as long as we have one of its disjuncts as true.

4. Disjunctive Syllogism (D.S.)

p V q; ~q /:.p

OR

p V q; ~p /:. q

If one of the disjuncts is stated to be false, then the remaining disjunct is true.

5. Modus Tollens (M.T)

p q; ~q /:. ~p

If the consequent of a conditional is false, then its antecedent is also false.

6. Modus Ponens (M.P.)

p q; p /:. q

If the antecedent of a conditional is true, then the consequent is also true.

7. Hypothetical Syllogism (H.S.)

p q; q r /:. p r

If the antecedent of a conditional leads to an antecedent of another conditional, then you can infer that the first antecedent leads to the consequent of the second conditional.

8. Rule of Dilemma/ Constructive Dilemma (C.D)

p V q; p s; q r /:. s V r

If either of the antecedents of two conditionals is true, then either of their consequents must also be true.


Alright, off to examples! We’re gonna start off easy and build onto harder and longer proofs.





Alright, now on to real problems; I have included two. I’ll give you guys the premises and the desired conclusion and I’ll post answers on how to derive the conclusion on the page after that. On to the next page!

Plato’s Republic Books IV-IX: An Analysis Essay

*This is for educational purposes only. All who plagiarise or otherwise attempt to reproduce this content will be prosecuted to the full extent of the law. *
This was written for a PHIL2010 class and I didn’t get a 100% on it so if in doubt, please refer back to the original material.

A/N: I originally decided to post these three essays on Outlet while I was writing this essay as the final for my class. I thought about the state of America and I thought about the trending thoughts and concerns of the world and the pushback of these thoughts and concerns. So, please read this essay with those thoughts and concerns in mind. In a lot of ways, Plato has hit the head on a lot of issues in his own way even though Athenian culture and attitude is supposedly far removed from how things are today.

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Socrates’ Tripartite Theory of City and Soul

Reconstruct in your own words the chief arguments by which Socrates justifies the theory of a three-fold soul and city.

++++++Socrates argues for a three-part city and soul in his theory of how justice can be realised. He first builds the city based on the principle that the city takes on the characteristics of its citizens and that since the city is a bigger entity, is easier to spot where justice and other virtues lie (Book 2, 368d-369a). First, the city is founded on the idea that individuals aren’t self-sufficient and therefore need to band together to provide all the goods that one needs to survive, giving rise to the principle of the natural division of labour (Book 2, 369e-370c). These people are the first defined part of the three: the craftsmen. The next group that arises are the guardians who are needed as the city grows and is now in need of military power (Book 2, 372e). Lastly, a third group is created out of the guardians, splitting the guardians into the auxiliaries that make up the armed forces and true guardians that will act as overseers or rulers in the city (Book 3, 412a-e). With these three classes established, we can then start looking at where the virtues of the city lie and most importantly, where justice lies. The virtues are defined as wisdom, courage, temperance and justice (Book 4, 427e). The rulers display wisdom in their ability to use their knowledge to know what is good for both the parts and the whole of the city (Book 4, 428a-429a). Courage is displayed by the auxiliaries being knowing of what to fear and not fear in to preserve through both pain and pleasure to faithfully execute their duty (Book 4, 429a-430c). Moderation is displayed when the citizens of the city submit to the reign of the guardians and this produces harmony within the city between subject and ruler (Book 4, 430c-432a). Lastly, justice can be found where the other virtues are not, revealing itself in each part of the city faithfully carrying out their job and that to do otherwise can be considered to be unjust (Book 4, 432b-434c).

++++++With the city and its virtues fleshed out, we can then move on to the soul. The underlying principle of the division of the parts of the soul lies in the fact that one thing cannot be willing to do or be the opposite relative to the thing in question on the same subject (Book 4, 436b-437a). Therefore, if a soul is displaying opposing desires, then there must be multiple parts to that soul that are generating those independent desires. Socrates then set about defining these parts using an analogy of a thirsty man.

++++++The first part of the soul to be defined is the appetitive part where the man is simply desirous of a drink. There is no reason to it; it does not desire a good drink or a healthy drink, merely a drink (Book 4, 437e) because to want a good drink means that it’s no longer an appetitive desire and requires a reasoning element to know what is good and healthy (Book 4, 438a-e) and therefore all of its desires needs to be unqualified (Book 4, 439b).

++++++This leads us to the second part of the soul, the rational part. With the desire to drink can come with the opposing disinclination to drink (Book 4, 429c). This part uses reason to rein in the desires of the appetite. For example, while the appetite may desire a drink,  reason will stop it from drinking pond water which could have caused harm to the body.

++++++However, reason doesn’t seem to be the only part that has control over the appetite. This can be seen in the fact that having given in to a desire against reason, a person may experience anger for having done so and thus, exposes a third part of the soul that seems to aid reason in controlling the appetite (Book 4, 440a). The third part comes into being with the observation that small children and animals seem to still display some amount of control over their appetites despite not having a fully-formed rational part of their soul. This third part of the soul is the spirited part — an honour-loving part that gets angry when one indulges in one’s unbridled desires. Since the spirit part can exist without the rational part, this means that the two parts are separate despite both of their purposes being to control the appetite (Book 4, 441b).

++++++With all the parts of the soul established, we can begin to apply the virtues to the soul as well. The rational part of the soul would naturally be where wisdom is exhibited by its use of reason to make decisions for the rest of the soul (Book 4, 442c); the spirit would exhibit courage by also preserving through pain and pleasure to know what is worth fearing (Book 4, 442c); moderation can be found when the parts of the soul are in harmony with one another and justice is exhibited when each part is properly performing their role with the proper balance between all three parts (Book 4, 442d). With this, Socrates divides both the city and soul into three parts and is able to draw corresponding parts between them.

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Obstacles to the Realisation of the Just City

Identify the problems that Socrates recognises to jeopardise the realisation of justice in the polis and soul.
Evaluate to what degree Socrates succeeds in showing that justice can be achieved in both polis and the soul.

First Obstacle: Against the Equal Treatment of Men and Women

++++++However, even with the source of justice found in both the city and soul, Socrates’ interlocutors aren’t convinced that a truly just city can exist. The first of three complaints are directed towards the fact that women seem to be given the same responsibilities within the city as the men and they argue that that can’t be so because women are of a different nature than men. They drew particular attention to the fact that men and women in this city were to train together in the typical Greek nude and thought it a ridiculous notion (Book 5, 452b). However, Socrates argues that since only those best at a task can perform that task, this requires that all guardians have the same education ( Book 5, 451e) and since this is good and the proper way to maintain justice in the city, the idea cannot be ridiculous (Book 5, 452d-e). Socrates further supports his position on having women as part of the guardians by likening the situation to one of a bald shoemaker and a long-haired shoemaker. He asks if the presence or absence of hair, in either case, precludes one or the other from having the proper nature to perform the job of shoemaking.

++++++Having established that it is a ridiculous idea, it is agreed that since women do not differ from men in the significant ways that would make one more or less suited to a particular practice, then there is no reason to limit women to or from specific practices (Book 5, 454c-e).  This argument maintains that since the woman, although generally physically weaker than man, is made of the same three parts of the soul and so, is able to have the same natures relevant to the types of jobs that the city needs to sustain itself and therefore, upholds the existence of justice in the city as both men and women are able to perform the job best suited to their nature, including becoming guardians (Book 5, 456d-457b). Therefore, the inclusion of women in the guardians and in all other roles of craft is both plausible and beneficial to the city.

Second Obstacle: Against Families Being Held in Common

++++++The second of the three complaints of the city is directed at the system of common spouses and children within the guardians. Socrates asks for the assumption to be made that the system be considered plausible to allow him to address whether it is beneficial (Book 5, 457e-458b). Having been granted that assumption, Socrates starts with saying that since the men and women would be rooming together, it’s natural that they would have sex with each other. However, if left unregulated, it would harm the city by introducing extraneous loyalties into the guardians so the city should regulate it to achieve maximum benefit (Book 5, 458c-e). Since we would want to produce the best guardians for the next generation, then only the best guardians in the current generation should be allowed to procreate with one another, just like how dogs and livestock are bred for favourable traits (Book 5, 459a-b). This would cause disunity within the guardians as it would be a form of favouritism so they would need to be deceived. They would be told that their right to get married and, by extension, to procreate is determined by lottery. This also allows the city to manage the population so that while the city doesn’t overpopulate, there are also enough people to sustain the city if there was war or some other extraordinary circumstances.

++++++However, the city cannot prevent those seen as possessing not the less than favourable traits from procreating so their children must be disposed of in secret. Since children are held in common where the child doesn’t know who are their parents and vice versa, this is possible to maintain the absolute integrity of the guardians’ offspring (Book 5, 459c-460d). Furthermore, only men and women in their prime years should be allowed to have children sanctioned by the state. Those who procreate outside of these years will also have their children be disposed of. Since familial relations aren’t known, to prevent incest, those of different generations won’t be allowed to marry and procreate (Book 5, 460e-461e).

++++++By demonstrating the way in which common families can be carried out, Socrates can turn to show that it is a beneficial arrangement. The idea behind this arrangement was to bolster unity within the guardians of the city so that their loyalty would be to the city and not to spouses or children. The arrangement would allow the guardians to share a sense of commonality within themselves and all things held in common where pain and pleasure are shared by the whole of the group (Book 5, 461e-462e). The guardians have the most ability to split the city as they are the group with the means and knowledge to wage war. If the guardians are united, then the city is safe from internal dissension and protected from foreign forces (Book 5, 465b). Furthermore, since spouses and children are held in common, each guardian would be inclined to fight hard no matter who they’re next to in battle, not valuing one life over another (Book 5, 466e). This ensures the survival of the city as a cohesive whole and is therefore considered beneficial. It also ensures that the guardians are only focused on their loyalty to the city and performing their duties so an arrangement like this upholds the justice of the city by allowing the guardians to focus only on their job and to perform it at all times as dictated by the natural division of labour.  

++++++However, by bringing in eugenics, he does slightly undermine an idea he introduced previously in his first noble lie: the Myth of Metals (Book 3, 415a). The Myth of Metals posits the idea that all citizens are born with a metal that corresponds with a particular class within the city: bronze and iron for craftsmen, silver for auxiliaries and gold for true guardians. If the idea is that people are naturally born with a certain metal and the metal a person is born with is random, then the fact that the guardians are bred with the result of their offspring having the best metals in mind, then it calls into question whether the “metal” is something inborn and random or something that can be bred. However, on further thought, although there does exist this contradiction, the noble lie is still a lie to fool the general populace so it was never supposed to be taken seriously by the rulers who are imposing these systems and noble lies and because of this, Socrates’ arguments still stand without much opposition.

Third Obstacle: Against the Plausibility of Such a City

++++++With the first two of the three waves of complaints addressed, the last wave of complaints addresses the conception of the just city itself in the form Socrates has built (Book 5, 471c). Socrates then introduces the argument that for such a city to exist, either kings must become philosophers or philosophers must become kings (Book 5, 473c-e). He argues that if rule and philosophy were united, then the just city can exist. To demonstrate that such an arrangement is possible, we would have to first address what it is to be a philosopher (Book 5, 474a-b).

++++++ First, Socrates says that a philosopher, as a lover of wisdom, must love all forms of wisdom and not just towards a specific subject (Book 5, 474c-475e). However, true philosophers are lovers of truth so this directly contradicting the previous claim. Socrates resolves this by pointing out that since truth can only be known when one has grasped the Forms (what it means to be completely Good or Beautiful or Just etc), philosophers only possess true knowledge on all fronts and not just an opinion or belief based on perception about specific subjects when they can grasp “what is completely” (Book 5, 475e-476d). Such philosophers would be virtuous because, above all, their seat of reason is in control over other desires and this results in the philosopher being a just man with the rest of his soul falling into line and by extension, displaying all the other virtues like a city and soul who has all three parts in proper alignment with the rational, aided by the spirit, lording over the appetite. So, by defining philosophers thus, he distinguishes “pseudo-philosophers” that are lovers of sights and sounds from those true philosophers who have grasped the Forms and therefore true knowledge and, possessing the virtues, are then fit to rule (Book 6, 484a-d).

++++++The next problem then is to address how such philosophers should come to rule as Adeimantus points out that the people won’t willingly follow a philosopher-king because the opinion of the people on philosophers are of those who turn their knowledge and abilities to vicious acts, or, for those who remain pure in their craft to be useless to the city, blind to everything but their quest for knowledge (Book 6, 487a-d). Socrates agrees but he posits that the few philosophers who possess a true philosophical nature aren’t nurtured correctly. He claims that if such philosophers were given proper conditions and allowed to learn and grow in such an environment, their natural talents wouldn’t be corrupted to be used in politics or sophistry and they would be willing to take on the mantle of rule (Book 6, 497a-b).

++++++There is still a question of how such an environment would arise as these philosophers can only be reliably be brought about by the very city that they must already rule over. To this, Socrates insists that it is not impossible and it is only the current unfavourable opinion of the people on philosophers that rendered the idea implausible (Book 6, 499a-500e). To make people more accepting of such a ruler as well as making the emergence of true philosophers as rulers, education would be key. The easiest way to do this would be to reach the children of the city young and eliminate the influence of other adults by sending everyone over the age of ten out of the city and educating the remaining children (Book 7, 541a-b) in the arts, dialectics, mathematics and astronomy as well as physical training in a specific order and at certain times in their lives (Book 7, 524d-540c). Of course, only those who have proven themselves to be potential candidates to be rulers are going to go through the full course of such an education and most people won’t be trained in all the aforementioned subjects in full and instead become auxiliaries or craftsmen. With the proposed arrangement of sending all but those who are ten or older out of the city, Socrates’ defence against this third wave ends, having proven that the city as it is described right now is possible and given the arrangements so far made, that they are beneficial.

++++++However, despite the glaring implausibility of a city of children under ten years old, Socrates never addresses this. This proposal creates more problems than it solves. Without the adults in the city, the city cannot sustain itself. If the adults were to be removed outside the city and still somehow be able to carry out their crafts, then it remains to be answered the location and duration. Even with Socrates being able to clear up the first two waves of criticism about the city with relative effectivity, in introducing this last arrangement, he has a glaring implausibility still needing to be accounted for. Without a proper conclusion to this argument, since the existence of the city is precipitated on whether the children can be raised in the way described, the very formation of this city is threatened and the justice that Socrates was trying to create falls short of realisation.

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Democracy: Second Worst

Explain why Socrates considers democracy and the democratic man to be the second worst types of injustice

Note: The word aristocracy is from the Greek roots, aristos, which means excellent, and kratos, rule. Therefore, the word aristocracy as used here refers to a meritocracy where rulers are chosen based on ability.

++++++With the city established so far, we return to the discussion of justice and the forms of injustice that may arise in the different constitutions that may arise in this city. Since the city is a reflection of its citizens, then we can speak about the presence (or lack thereof) of justice in both the man and the city and see which is the most unjust and whether injustice corresponds with happiness or misery (Book 8, 544d-545c). Socrates proposes five different cities, including the current constitution of the just city. One of these constitutions is one of democracy and the corresponding democratic man. Socrates will later claim that this is the second worst type of injustice and therefore, the second unhappiest constitution.

++++++To see why, we will first have to understand what other constitutions there are. The original form is aristocracy where everyone performs the job they are naturally suited for. This is the optimal constitution of a just city and because justice is present in its fullest form, the aristocratic man and the aristocracy are the best. Serving as the basis from which we are going to explore the other less good, less just cities, the other cities will see a deterioration between the balance of the three parts of the city and by extension, to the soul of the individuals who have that constitution and then, we will compare to see who is the happiest (Book 8, 543c-544d).

Three Types of Desires

++++++To do this effectively, we would first have to look at the three different types of desires: the necessary, the unnecessary and the lawless desires. The necessary desires are those that are required to survive and the unnecessary desires are those we can survive without and thus, with proper education, can be conquered (Book 8, 558c-559d), and unlawful desires are those desires without limits and seek to be satisfied at the expense of everything else. We will expand on these desires as they arise in seeing how the city deteriorates from its just form.  

Timocracy

++++++The first sign of this deterioration comes in the form timocracy where the guardians of the city neglected the arts (poetry, music etc.) in their studies and become more warlike and start obsessing over the accumulation of wealth. However, even though their reason is starting to crumble and giving away to their appetite, their spirit keeps their desires in check for the most part and their activities to accumulate wealth are kept secret to maintain their honour. They seek glory in battle and war and this forms competition within the guardians which then breeds dissension within their ranks (Book 8, 545c-549b). The timocratic man is torn between following his aristocratic father, who encourages his use of reason, and his peers, who encourage him to seek honour and recognition (Book 8, 549c-550c). This is one step down from aristocracy because the authority of reason and its aid, spirit, has been weakened by internal dissension and due to this, the appetite is then able to exert more of its influence in its desire for honour and wealth.

Oligarchy

++++++The next constitution to arise is oligarchy where owning a certain amount of property become a requirement to hold office and the guardians’ preoccupation with wealth becomes apparent (Book 8, 550c-551b). The city then becomes divided between the rich and poor. Since the rich are few and the poor are many, they mistrust those who aren’t rich and this will cause them to undermine the power of the auxiliaries for fear that they will be supplanted, weakening the defence of the city and its ability to wage war. In this city, the man’s role in the city isn’t reflective of his nature and his status is purely reflective of his wealth and thus, the people filling certain jobs aren’t adequately doing those jobs and those who should be doing those jobs can’t without sufficient status as it is in the case of rulers. This creates unemployment in the city and gives rise to the drones who are divided between the stingless beggars, and the thieves and other criminals with stings (Book 8, 551b-552e).  

++++++The oligarchic man is characterised by a fear stemming from his timocratic father losing his wealth and status and thus begins obsessively hoarding wealth. However, besides his need for more and more wealth, the rest of his appetite is suppressed because, to satisfy other desires, he would have to sacrifice part of his wealth. In other words, he only indulges in his necessary desires and keeps unnecessary desires in check. This is the next step in the city’s deterioration because appetite is starting to clearly dominate reason but only in one respect. In all other desires, the oligarchic man still has an iron grip. Like how he is unwilling to indulge in his other desires to accumulate the most wealth, the oligarchy tries to weaken the auxiliaries to maintain their authority. Furthermore, like the city, the soul of the oligarchic man is divided into two where his need for money is set against all his other desires (Book 8, 554a-555a). Justice is now severely threatened if not nonexistent in both the city and the soul as people, especially the rulers, aren’t taking up the jobs they’re most suited for and there are those who have no job in the city and the seat of reason/wisdom is no longer the sole ruler of either the city or the soul.

Democracy

++++++Following oligarchy comes democracy which Socrates claimed was the second worst form of the city and soul. Here, the poor of the oligarchic city has risen up in revolution against the ruling rich who, weakened by extreme greed and faulty business practices, lose their status and a government is established where self-rule is practised (Book 8, 555b-557a). In this city, all desires are considered equal and there is no longer a distinction between what is supposed to be the seat of reason (the rulers) and the appetite (the wants of the city). The government no longer pursues what is best for the city but rather, the impulses of the majority and suppresses the minority. Since there is no longer any restriction on the appetite, people do as they wish and everyone is considered equal. Whereas the oligarchic man still had a handle on his unnecessary desires for his quest for wealth, his son, the democratic man, begins to long for the goods that the money could buy to satisfy his unnecessary desires and at the urging of others, gives in to those desires. In time, he moderates his more extreme desires and grows to treat all his desires as equal (Book 8, 557b-558c). In the democratic city, more of the virtues are upturned as temperance no longer exists as the ruled and ruler become one and the same. As education becomes less and less of a priority, wisdom and courage are no longer displayed as the proper knowledge to know the truth or to know what to fear is no longer taught and a similar transformation takes place between the soul of an oligarchic man to a democratic man with the spirit and reason brought down to the same level as the appetite.

Tyranny

++++++This leads to the worst constitution for the city and soul: tyranny. Division is created within the city when those who are trying to acquire wealth and status are accused as being enemies of the people and in response, those people will try to act like oligarchs by suppressing those below them. Out of this struggle, the people will nominate a champion for their cause and this champion will become the tyrant. In the democratic city, the breakup of the three parts of the city becomes the drones, the wealthy and the rest of the common people. The drones, hoping to gain the riches of the wealthy for themselves, will prey on the sensitivities of the masses and orchestrate an uprising using the overwhelming momentum of the masses united under a cause and uses this conflict between the wealthy and the masses to seize power (Book 8, 564b-566d).

++++++A city under a tyrant is always in turmoil as the tyrant endlessly stir up fears that there are enemies to the people to keep the people distracted to consolidate his power and control. He wages wars and tries to eliminate all dissenters and people of wisdom and insight because they threaten his hold on power. Therefore, his citizens have the least freedom and are the least happy. Although he is able to indulge in all his desires, (even those lawless desires that one would act out only in dreams, Book 9, 571a-572b) he is constantly in fear of opposition and assassination, and cannot trust anyone (Book 8, 566d-569c)and so, is the unhappiest (Book 9, 576b-580a). The soul of a tyrannical man is the same. All that rules his soul is his appetite fueled by erotic love. Neither spirit nor reason remains to restrain his desires and all virtues have long since ceased to exist, making him the most unjust of men (Book 9, 572b-576b).

++++++Having seen all five constitutions of the city and soul, we can now look at why democracy and democratic man is second-removed from being the worst constitution. Whereas the democratic man still possesses his reason and spirit in conjunction with his appetite, the tyrant is only aware of his appetite, making democracy above tyranny and therefore not as unjust as the tyrant. It is below the other three constitutions because there is no distinction in the roles between the three parts of the city or the soul as they are considered equal in the name of total freedom, making the democratic city and man more unjust than the previous three constitutions and thus, the second unhappiest (Book 4, 443d).

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Socrates’ Critique of Democracy and Self-Rule

Evaluate Socrates’ critique of democracy and democratic man.
Discuss whether Socrates’ argument concerning self-control in Book IV repudiates self-rule and whether justice can be realized in the soul of each citizen without making each eligible to rule

++++++Besides that, democracy’s concept of self-rule also goes against some of Socrates’ previously proposed truths. Previously, Socrates talked about how the parts of the soul is to be in proper order. He said that there must be a stronger and a weaker part of the soul and a better and worst part of the soul. If the better part is stronger and rules over the worst, then we can say that the person is in control. If the opposite is true, then the person is said to be self-defeated (Book 4, 431a).  In the aristocratic city, only those worthy of ruling and possessing the knowledge to rule are the rulers while the others are subjected to their rule, and therefore the city can be considered to be self-controlled (Book 4, 431b). In the democratic city, uneducated or not properly trained individuals can become the rulers and by representing the democratic spirit of considering all desires equal, will rule according to wherever his impulses take him. This shows that self-rule isn’t a good way to rule a city as it allows the indulgence some of man’s worst impulses and when congregated in greater numbers, causes majority rule to not reflect what is best for the city or even what is good but are rather often random and irrational as pointed out in The Crito.

++++++Lastly, we must discuss what separates a just individual from a ruler. There is more than just the education that has been before mentioned in Book III that separates a just man from one fit to rule, there is also, more importantly, the question of a person’s nature. While an education can heighten one’s natural aptitudes, a person’s nature is inborn and hard to change. Socrates lists several traits that rulers would need to have: having a good memory, a quick learner, personable, and a friend of truth, justice, courage, and moderation ( Book 6, 846e-847a). Furthermore, a ruler would need to be able to grasp the Form of the Good. If the rulers can grasp the Good, then they are then able to grasp the other Forms (Book 6, 504d-505a) just as the Sun provides the light to makes vision possible to perceive the things around us, the Good illuminates the being of the Forms, making them knowable ( Book 6, 507a-509c). Since the knowledge of the Good allows one to reason without having to rely on previous assumptions or their senses, then that means that those who can grasp the Good are able to get at true knowledge and not merely superficial knowledge derived from appearances or formed from deductions. This allowed the rulers to know what is truly good for the city and distinguished them from the auxiliaries or the craftsmen who had a lesser education and less of an inclination towards the seeking of truth or knowledge.

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Works Cited

Plato, and John M. Cooper. Complete Works. Hackett, 2009.

Logical Biases: Preserving Fact from Perception

Today, we’re going to be talking about biases our brains have when processing information. This is important to know about because of the political and social environment we’re currently in. We have to know why some people think the way they do and how they manage to maintain irrational beliefs despite overwhelming evidence that their beliefs run contrary to facts. In fact, these logical shortcomings are so prevalent that even scientific professionals have to guard against them. However, when ordinary people fall victim to them, it’s much harder for us to self-diagnose and control for these subconscious biases and it often ends up in misunderstanding and misinformation. I tell you, our subconcious’s fear of cognitive dissonance is something to be feared (and rightly so).

However, it is not only an individual’s fault for falling into the trap but what we’re being exposed to in the media, in the social circles we’re part of and what authority figures tell us to think can also perpetuate these widening ripples of falsehood.

1. Confirmation Bias

In science, when they conduct experiments, researchers try not to let their own predictions on the outcome of the experiment affect the actual outcome of said experiment. When you seek out information that specifically confirms your own beliefs and pass over or completely ignore information that goes against your beliefs, that bias is called confirmation bias. This clip from a CH video explains this quite well and it also helps explain the vaccine = autism mindset some people have nowadays.

For researchers, they attempt to avoid this bias by either developing an objective way of measuring results or by performing blind or double-blind studies where the participants of experiments and the researchers that are directly observing the results of an experiment don’t know what sort of result is expected and therefore doesn’t skew the actual results of the experiment.

Then, there have been researchers who knowingly skewed the results of an experiment to confirm a result beneficial to their agenda. For example, back when obesity first showed its advance on modern society in the form of heart disease, a theretofore uncommon condition, people were trying to find something to blame. Fat became the victim while the sugar industry got a free pass. When people found out, a man by the name of Ancel Keys got most of the blame.

Here’s a (slightly biased) video about the whole incident…

 

…. and a more objective review of the whole affair outlined here from a fellow denizen of WordPress:

The Truth:

  • Ancel Keys did not drop any countries from the Seven Countries Study. His most famous graph—the first one up above—is from a different paper he presented at a World Health Organization (WHO) conference in 1955. The Seven Countries Study didn’t even launch until 1958, and entailed much more than just plopping numbers into a pretty curve. (That said, the Seven Countries Study had plenty of problems too; some are mentioned on this site.)
  • Contrary to popular belief, the cherry-picked graph didn’t convince everyone that fat was evil. In fact, Keys was pretty much ridiculed for the weakness of his fat/heart disease theory by other scientists at the WHO meeting, and whenever his graph was cited in medical journals later on, it was usually paired with some criticism. Although Keys’ work definitely shaped our current beliefs about fat, this graph didn’t exactly take the world by storm. (More on this later.)
  • When all 22 countries were analyzed, the association between fat and heart disease did not go away. It actually remained statistically significant (meaning it probably wasn’t due to chance). And to make matters worse, the paper frequently cited as a “rebuttal” to Keys shows pretty clearly that animal protein had an even stronger association with heart disease than total fat did. The China Study was right all along! Time to go vegan, you guys. (Just kidding. But this part is the most interesting of all, and we’ll examine it in excruciating depth in a moment.)

Although some of his saga has been misconstrued, Keys was still far from perfect—and his eventual role in demonizing saturated fats (while glorifying polyunsaturated fats) has led us down an unfortunate road.

Click here to see the whole article. (Kudos to the author for such thorough research.)

The fact that Keys’ own bias could have gotten in the way of objective research is something that everyone can learn from and avoid. So just be careful to know the whole story when looking at an issue or an event and don’t surround yourself with only sources or people who agree with you.

Here’s a good source to learn more about this bias.

2. False Consensus Effect

You know a person who is clearly wrong but is so sure that they’re right that they assume that everyone else thinks they’re right too? This is called the false consensus effect. This is especially crucial if you’re in a position of power. A person with decision-making powers over other people may make decisions for other people and assume that their subordinates (or constituents, for that matter) agree with them. This makes people less likely to actually seek out the opinion of others and it also leads them to create a bubble of “yes” people around them, furthering the delusion.

See here to learn more about this effect.

The false consensus effect is also tied to another logical fallacy which we will expand on next…

3. Availability Heuristic

This is our brain’s tendency to look for information that is easiest to get. This is why news and other media outlets aren’t the most reliable sources when it comes to forming conclusions about the world. Since what the news covers is limited and focuses on certain stories by nature, what we do hear about will seem bigger and more prevalent than the stories that we don’t hear about. For example, shark attacks are often sensationalised and when it does happen, the news outlets report on it. However, as the popular comparison goes, more people die from incidents relating to vending machines than shark attacks (see here for far more likelier ways you’ll die). But people are still more paranoid about being attacked by sharks than dying from vending machines. This is because there is more information and instances available to draw upon since you were more exposed to it.

This is especially important when it comes to making decisions and other social phenomena like mass hysteria. This is also why propaganda works. When given lots of examples to hate and fear the Japanese and the Chinese (each at different times in US history), the public ate it up and adopted the hate with posters like this:

US_propaganda_Japanese_enemy

15-exploding-brain-meme.w710.h473.2x

images.jpg
Titled The Yellow Terror in all his Glory

And this was before television became popular. So… you can imagine the impact of television now.

Then, to tie it back to the false consensus effect, when people make a conclusion based only on information they’re exposed to and are unaware of any other information, then it lends itself to false confidence in their beliefs and when they expouse* these beliefs to a group of people who are less sure, this belief then spreads into the misinformation epidemic we face today.

For a full list of all biases, see here.

Well, that was all for today. Don’t forget to like and follow! We’d love to hear what you think of this topic.

This is Lieutenant out.

*Expouse is a word coined by me. The official definition is:

Ex•pouse /ik•spous/

Verb

  • (usually of a political or religious belief) to spew with great conviction

The Ultimate Logical Loophole: The Devil’s Proof

Out of all the potential fallacies and blind corners that logical systems of thought often make, the most frustrating is the occurrence of what is called The Devil’s Proof. With this, anyone can claim the outrageous and lay waste to scientific research and logic.

To put it simply, the Devil’s Proof is the fact that non-evidence cannot disprove something’s existence. While evidence can help prove something, the lack of evidence cannot prove that something is untrue. While scientists have ample evidence that autism is not connected to vaccines, however, because of the Devil’s Proof, they cannot confirm 100% that autism is not linked to vaccines. As one scientist put it:

“[While I can’t disprove the link between autism and vaccines,] I am as certain that autism is related to vaccines as I am that I will fly if I step off the roof of this building.”

Using this logical loophole, people can claim anything because unless it has been proved to be something else, anything could be everything and vice versa. That might sound confusing and hard to swallow because our brains like to think that what we know to be true is definite. However, since we need affirmative proof to officially say something exists or exhaust every method possible to prove that there is no proof, everything that does not have evidence proving its existence can also be true because maybe the reason why we don’t have proof yet is just because we haven’t discovered it.

Here’s another example: If your friend shows up with a candy bar that you just lost, can you know that their candy bar was stolen from you? In a legal scenario, the lack of evidence that she took your candy bar means that you technically can’t indict her for the crime. However, due to the Devil’s Proof or what lawyers call probatio diabolica, she has to then prove she didn’t take your candy bar by showing where she got it from etc. So in a court, when faced with proving something impossible to prove, the burden is then reversed onto the other person to prove their innocence.

This may be contrary to “innocent ’til proven guilty” but there is no choice when you don’t can’t definitively say that this person was the one who committed the crime but is instead just the most likely one. While the example above was somewhat simplified from what you see in real life, the Devil’s Proof, when applied elsewhere, isn’t so easily remedied.

You can see that in the belief that America has millions of the dead and “illegals” that voted in the last election. While there were four cases of documented voter fraud (three of which came from Trump voters trying to prove that there is voter fraud and got caught), the Devil’s Proof states that just because there is no further evidence doesn’t mean that it did not occur. Therefore, people have taken advantage of that and that’s how we ended up with this debate nowadays.

The same goes for conspiracy theories like the fact that the global elite might be lizard people from the Illuminati. There is absolutely no proof of that but, once again, the lack of proof doesn’t mean a seal of innocence.

While this sounds quite grim for those who are logical-minded, remember that while this phenomenon can be used to support whack theories, it also means that things like extraterrestrial life are very possible and so are some of the more tentative theories in quantum physics and the possibility of parallel universes etc. So don’t lose hope and remember that although this logical loophole can be dangerous in the stupid hands, it also opens up the world of possibilities.

While I’m sure most of you are already aware of the Devil’s Proof, you just didn’t have a name for it. Well, here it is. Hope you guys enjoyed this article and leave a like if you did. Follow for more of this sort of thing and comment any topics you would like us to cover.

This is Lieutenant and I’ll see you next time.

P.S. School starts next week so I’ll have to rebalance my schedule between school, work, fencing club and writing for Outlet. Expect a rough patch in the coming weeks. I don’t think I’ll have any major problems but who know… Well, I wish anyone going back to school this fall luck and godspeed to you all.