Talons Philosophy

An Open Online Highschool Philosophy Course

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Logic Assignment Introduction

Logic Lane, Oxford

Photo of Logic Lane at Oxford by Andy Hough on Flickr.

As we move into our unit on logic, the face-to-face participants in Philosophy 12 have been reading about the Basic Concepts of Logic (pdf), which may be defined as “the science of reasoning.” Delving into statements, premises, propositions, as well as truth, validity and soundness, our hope is to greet the weekend with a host of blogged examples of logical arguments in their natural habitat. In past years, the tasks around logic have involved a similar feat of strength, and participants have generated multiple examples of logical arguments and tested them for form and content. Occasionally this has sparked interesting discussions of both the merits of this or that argument, the cultural implications (or origins) of such thinking, and by amending the unit assignment this week hopefully we will see more of this type of discourse emerging around our logical examples.

The Assignment 

  • Summarize and describe an example of a logical argument you have uncovered in a variety of settings: current events, popular media, personal anecdotes or hypothetical thought experiments. Be sure to include enough back-story for people unfamiliar with the milieu of your example to digest the logic at work, and provide links, video, or attached materials so that your audience can follow up or extend their inquiry into your example with ease.
  • Dissect the argument and its form by representing it as a syllogism.
  • Evaluate the argument for Truth, Validity and Soundness and explain your judgements.
  • Reflect upon the origins or implications of your selected argument. Where does it (or others like it) come from (in society, culture, etc)? What are the consequences of the conclusion drawn, or from the argument being framed in this way?

Post your example on the class site no later than Tuesday morning, and be sure to include the proper Category: Logic and Scientific Philosophy.

For your reference and preparation, here is an example of a response to this assignment:

Prime Ministerial Logic 

Image via Transitions, an Advocate for Sociological Inquiry

Following the discovery of Tina Fontaine’s murdered body in the Red River, in August, Prime Minister Stephen Harper faced reinvigorated calls to launch a federal inquiry into murdered and missing aboriginal women in Canada. On the heels of reports from the special rapporteur to the United Nations, as well as the RCMP, which each discovered that aboriginal women in Canada face significantly higher rates of violence than non-aboriginals, Harper’s federal Conservative Government continued to reject pressure to better understand the root causes of this trend. The Prime Minister himself stated that “we should not view this as a sociological phenomenon. We should view it as a crime.”

The Prime Minister’s statement might be seen as an argument broken down to the following premises and conclusion:

Premise 1: The murder or abduction of aboriginal women is a crime.

Premise 2: Crime is not a sociological phenomenon.

Premise 3: A federal inquiry into murdered and missing aboriginal women would rely on sociological practices of inquiry.

Conclusion: Therefore, a federal inquiry into murdered and missing aboriginal women would not address crimes against aboriginal women.

By evaluating the various premises’ truth and/or accuracy, we might be able to reveal the soundness of the Prime Minister’s argument.

  • Premise 1 can easily be accepted as true.
  • Premise 2 can be more easily contested, as the study of criminology itself is a branch of sociological inquiry. While it is the government’s prerogative to define and combat crime in terms it was elected to uphold, practitioners in the fields of both sociology and criminology would likely contest the Prime Minister’s assertion that “crime is not a sociological phenomenon.”
  • Premise 3 can be seen to be true, as an inquiry into the trend of murdered and missing aboriginal women would “study social behaviour, its origins, development, organization, and institutions,” which Wikipedia defines as sociology.

As we can see, the flaw in the Prime Minister’s argument is contained in Premise number two, and damages the conclusion reached. While the argument’s form may be valid, an error in its content damages both the truth of its premises and the soundness of the conclusion.

The origins of the Prime Minister’s logic are difficult to trace, though they might be seen in the political ideology of Neoliberalism. Writing in the Toronto Star, Jakeet Singh noted that the Prime Minister’s remarks were

“clearly trumpeting a standard component of neo-liberal ideology: that there are no social phenomena, only individual incidents. (This ideology traces back to Margaret Thatcher’s famous claim that “there is no such thing as society.”) Neo-liberalism paints all social problems as individual problems.”

The effects of this logic being brought to bear on crime and punishment in Canada can be similarly difficult to witness (somewhat ironically even, as the evidence to be found would reside within the sorts of sociological inquiries the Prime Minister is denying). However, Singh’s article describes the casualties of Mr. Harper’s ideology as our societal ability to perceive and confront injustice. “You see,” he writes, “Sociologists often differentiate between “personal injustices” and “systemic” or “structural injustices.” Personal injustices can be traced back to concrete actions of particular individuals (perpetrators). These actions are often willful, and have a relatively isolated victim.”

Structural injustices, on the other hand, are produced by a social structure or system. They are often hard to trace back to the actions of specific individuals, are usually not explicitly intended by anyone, and have collective, rather than isolated, victims. Structural injustices are a result of the unintended actions of many individuals participating in a social system together, usually without knowing what each other is doing. Whereas personal injustices are traced back to the harmful actions (or inactions) of individuals, structural injustices are identified by differential societal outcomes among groups. Sociologists call these “social inequalities.”

By refusing to view crime as a sociological phenomenon, those accepting the Prime Minister’s argument do so within a broader context which should trouble those who believe in our collective responsibility for one another’s well-being. “When we paint all social problems as individual problems with individual solutions,” Singh writes, “we also lose any sense of the social responsibility, rather than personal responsibility, that we need to address them.”

 

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Definitions

Truth – actual state of matter – applied to premise (if one premise is false, the conclusion is false.)
Validity – correct form – containing premises from which the conclusion may logically be derived.

Soundness
– Argument/theory is valid
– All of its premises are true

Example:
All men are mortal
Socrates is a man
Therefore Socrates is mortal

This argument is valid because the conclusion is true, along with the premises, and since the premises are true, this makes the argument sound.

An example of an argument that is valid, but not sound:

All birds with wings can fly
Penguins have wings
Therefore penguins can fly

Since the first premise is false, the argument, even though is valid, is not sound.

Syllogism

Categorical
Correct example: Pro

http://talonsphilosophy.wordpress.com/2012/10/03/jonathan-toews-a-famous-hockey-player/

Con

http://talonsphilosophy.wordpress.com/2012/10/04/bedtime-syllogism/

The argument of this example is not true, due to the premises being incorrect. The premises are not true, therefore makes the argument not sound. The conclusion of this syllogism however is valid, as the conclusion follows from the premises.

Disjunctive

Pro
http://talonsphilosophy.wordpress.com/2012/10/02/disjunctive-syllogismtouchception/

Con
http://talonsphilosophy.wordpress.com/2012/10/07/vonnegut-logic/

Fallacy

A fallacy is an argument/ statement based of false or invalid interference.

Example:
Penguins are black and white
Some old tv shows are black and white
Therefore some penguins are old tv shows

 

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She Turned Me Into a Newt!

 

 

The peasants in this video believe the woman is a witch. Why? “She looks like one.”

This, however, is not good enough for the knight, Sir Bedevere, a man of science. He proposes a simple way to determine her guilt.

What do the people do with witches? Burn them.
And what  burns, other than witches? Wood.
Well then, why do witches burn? Because they’re made of wood.
How do we find out, then, if she is made of wood?
Does wood sink in water? No, it floats.
What else floats in water? A duck.

So, logically…
If she weighs the same as a duck, she’s made of wood.
And if she’s made of wood, she is therefore a witch.

To summarize:

1. All witches are things that can burn.
2. All things that can burn are made of wood.
3. Therefore, all witches are made of wood. (1 & 2)
4. All things that are made of wood are things that can float.
5. All things that weigh as much as a duck are things that can float.
6. So all things that weigh as much as a duck are things that are made of wood. (4 & 5)
7. Therefore, all witches are things that weigh as much as a duck. (3 & 6)
8. This thing is a thing that weighs as much as a duck.
9. Therefore, this thing is a witch. (7 & 8)

There are many ways that these premises are invalid and this argument unsound, which have been further deconstructed here. But even at a glance, we know that not everything that burns is made of wood, weighing the same as a duck does not guarantee flotation, etc.

In the Monty Python world, this kind of logic exists often. It helps to introduce the type of humour used in Python as well as how ridiculous they can be. I find Monty Python’s use of humour to be quite entertaining and effective.

 

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After Some Revisions… – Kelly

I awoke this morning to an extraordinarily kind comment from Mr. Stephen Downes, who tore my blog post to shreds.  Well, that is slightly dramatic.  He opened my eyes to just how little I actually knew about how to properly write fallacy and syllogism.  So, after some reiteration, explanation, and revision, here is a (hopefully) more accurate version of what I tried to say last night:

Someone with the last name 'Bryant' is in Africa.
I am Kelly Bryant.
Therefore, I am in Africa.

While the two premises are true, this argument is not sound.

A – Bryant
B – Africa
C – I (Kelly Bryant)

This categorical syllogism follows the form of:

Some ‘A’ is ‘B’.
‘C’ is an ‘A’.
Therefore, ‘C’ is a ‘B’.

The two premises are true, but the form is wrong, making the conclusion false.  The form is wrong because there are two particular premises.  This argument is not vaild or sound.  My sister, Stacey Bryant, is currently in Uganda, so it is truthful to say that ‘Someone with the last name Bryant is in Africa.’  My last name is clearly also Bryant, making the second premise also truthful.

This is where the categorical fault in logic takes place. To categorize accurately, you would need to use the form of Disjunctive Syllogism:

Either Kelly Bryant or Stacey Bryant is in Africa.
Kelly Bryant is in Port Coquitlam.
Therefore, Stacey Bryant is in Africa.

This argument is both valid and sound.

A: Kelly Bryant
B: Stacey Bryant
C: Uganda

A disjunctive syllogism uses the following form:

Either ‘A’ or ‘B’ is a ‘C’.
‘A’ is not a ‘C’.
Therefore, ‘B’ is a ‘C’.

Typically, the word ‘either’ and ‘or’ mean ‘either or both’, not ‘either but not both,’ which makes this argument more difficult to accurately prove.  However, I began with saying ‘either’, meaning ‘one or both’ is in Africa, but then went on to say that one of the terms was in Port Coquitlam, making it clearly not in Africa.  This proves that the other term must be in Africa.  ‘Kelly Bryant’ (A) is clearly not in Africa, and one of the terms must be in Africa, so that soundly concludes that ‘Stacey Bryant’ (B) must be in Africa.

Stacey Bryant hanging out by the Nile in Africa

Kelly Bryant taking a nap in Port Coquitlam

 

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Bedtime Syllogism

All beds are for people to sleep on.
A riverbed is a bed.
Therefore a riverbed is for people to sleep on.

The conclusion of this syllogism is valid, as it follows the presented premises. However, this argument is not true, due to the untrue premises. As a result, this argument is not sound.

A: Middle Term = Beds

B: Predicate Term = For people to sleep on

C: Subject Term = A riverbed

This syllogism follows the proper form of a categorical syllogism: All (A) are (B). (C) is an (A). Therefore (C) is a (B).

Though at first glance the first premise may seem true, but due to its lack of clarity and specificity, it is not so. Without defining the word “bed”, the word can refer to any kind of bed, such as “roadbed,” “hotbed”, or “riverbed,” like in the premises. These examples are all some sort of base or foundation in which other materials or substances are placed upon, therefore all fall under the definition of beds. This disapproves that “All beds are for people to sleep on.” Therefore, the first premises is false. In order for this premise to be true, additional information is necessary. For example, if “that are designed for humans” was added on, it would now read: “All beds that are designed for humans are for people to sleep on.” “Roadbed,” “hotbed”, or “riverbed,” would no longer fall under this category of beds.

Though the conclusion is not true, one could still attempt to sleep upon a riverbed. Just because it isn’t for people to sleep on, doesn’t mean it can’t be.

 

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Zoe: Batman is On the Internet

Recently, a man named Stephen Downes has been leaving comments on this classes blog. After some thinking, I made a discovery.

All men who patrol their territory under his own power and initiative, strike fear into the heart of wrong doers in the dead of night, and does these things with only the tools and skills they has acquired through training themselves to extremely high levels are Batman.

Stephen Downes patrols his patrols his territory under his own power and initiative, strikes fear into the heart of wrong doers in the dead of night, and does these things with only the tools and skills he has acquired through training himself to extremely high levels.

Therefore, Stephen Downes is Batman.

As a basic syllogism, this is valid. It follows the pattern of

All A is B

C is an A

Therefore, C is B.
Whether or not the syllogism is true, however, relies on the validity of the two premises. First: All men who patrol their territory under his own power and initiative, strike fear into the heart of wrong doers in the dead of night, and does these things with only the tools and skills they has acquired through training themselves to extremely high levels are Batman. 

To show this premise as true, we have to prove two things: That this list of qualities is found in Batman, and that this precise list of qualities is not found in any other men.

The first argument, that the men must patrol their territory, rules out many men from the very beginning. As defined by Webster, the definition of patrol is “the action of traversing a district or beat or of going the rounds along a chain of guards for observation or the maintenance of security.”

While this does not necessarily mean that the patrol is lawful (as in the case of gang violence, perhaps), it does mean that someone who just happens to pass by a mugging in the street and steps in to help is exempt. To patrol, you must be traveling a certain area with the specific purpose of searching out any sort non-desirable behavior and either reporting it or stopping it.

If we look at the group of people who patrol, then, we can further rule out anyone who is part of an organization with the phrase “under their own power and initiative”. For example, police are exempt because they do not ultimately choose the area they patrol, or how much they patrol, or the procedures of the patrol. They may have some say of it, and the choose to become a police officer may relate to it, but in the end the final decision does not rest in their own hands. This also rules out organizations such as the military, gangs, and private security firms. We are left with only people who patrol completely of their own initiative. In other words, vigilantes, a “self-appointed doer of justice”.

We can now move on to the next part of the argument, where these so-called vigilantes “Strike fear into the hearts of wrong doers, but never kill”. Again, here we cut out any patrollers who attempt to stop behavior through ‘good’ acts, such as reporting them to authorities, or any patrollers who attempt to fight what they perceive as undesirable behavior with the death penalty. Fear, while seen as a very negative emotion, is not nearly so bad as death.

So now we have a man who consistently goes out at night to fight perceived injustice, and deals with these cases in a negative way for what he perceives to be the greater good (some sort of good, anyways, that provides him with the initiative to do it).

The last part of the argument is the clincher, wherein the man must not use any sort of superpowers or inborn advantage, but the tools and the conviction that he has  acquired trained himself in to an extremely high level. This rules out any sort of superheroes such as the Green Lantern or Superman, but it also rules out anyone who happens to patrol the streets at night out of the mere goodness of his heart, and does not have the skills to back it up. Average Joe who decides to make the streets better by striking fear into people’s hearts cannot be Batman; He does not have the skills or resources at the level that being Batman requires.

So no other man could or does do these things, but we still must prove that Batman does. That, happily, is quite simple. Anyone with a knowledge of Batman can tell you that he consistently travels the streets of Gotham seeking out injustice, which he combats in an entirely non-fatal but very terrifying way. Finally, he uses only the skills he has acquired through intense training, to world class levels.

The only man who patrols his territory under his own power and initiative, who strikes fear into the heart of wrong doers in the dead of night, and does these things with only the tools and skills he has acquired through training himself to extremely high levels, is Batman. Thus, the first premise is true.

Then, we have the second premise: Stephen Downes patrols his patrols his territory under his own power and initiative, strikes fear into the heart of wrong doers in the dead of night, and does these things with only the tools and skills he has acquired through training himself to extremely high levels.

With my limited knowledge of Stephen Downes, I suspect these all to be true. His territory is the internet, which he prowls with the knowledge that if he sees non-desirable behavior, he will put an end to it. We can see this from the recent slew of comments this blog has received from him, in which he combats the non-desirable behavior of faulty logic. As he is not part of any organization, nor is this blog any sort of immediate or non immediate threat, he is under his own initiative to do this. Through reactions from other students, I am able to see that he inspires a certain amount of fear, but there has been nothing fatal. A time stamp from one of his comments will show that he commented in what would be the dead of night in this time zone. And finally, Downes does not use superpowers, he uses the advanced knowledge and skills in philosophy and logic that he has trained to obtain. The second premise seems to be true.

There is only one conclusion.

Stephen Downes is Batman.

(Photo on left from here, photo on right from here)

 

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Gifted Individuals Proved “Ungeniuses”

All gifted individuals are geniuses.

Stephanie is a gifted individual.

Therefore, Stephanie is a genius.

Though this syllogism is valid, it is not sound as the information was based upon subjective opinions.  This statement is valid because it follows a correct form in which it includes a middle term “A” (all the gifted individuals), a predicate term “B” (geniuses), and a subject term “C” (Stephanie).  It is not a true statement or sound statement as the first premise is a false claim, because not all gifted individuals are geniuses.  Though many possess extraordinary traits, this does not necessarily mean all, including Stephanie, is a genius.

 

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Jonathan Toews, a Famous Hockey Player

Someone named Jonathan Toews is a famous hockey player

Jonathan Toews

I am someone named Jonathan Toews

Jonathan Toews

Therefore, I am a famous hockey player

Me, Jonathan Toews, the famous hockey player

 

This syllogism is both categorically invalid as well as not sound. Even though both premises are true, the two premises are particular propositions and do not relate to each other in a general fashion. This means that a conclusion cannot be drawn from them. Because the syllogism is not valid, it also lacks soundness. In this case:

A: Middle Term = Someone having the name  “Jonathan Toews”

B: Predicate Term = Famous Hockey Player

C: Subject Term = I

If this categorical invalidity were to be expressed in letters, it would look something like this:

A is B

C is A

Therefore, C is B

This is assuming that all A’s are B, which is not represented. In order for the argument to be valid, everyone named Jonathan Toews would have to be a hockey player (which would be a false premise). Unfortunately, this means I am not a famous hockey player.

 

 
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