Critical thinking exercise problem
Post Reply
 
Thread Rating:
  • 0 Votes - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
15-03-2014, 12:25 PM
Critical thinking exercise problem
I'm doing a self study course in critical thinking and I'm having some issues with an exercise. You guys need to help me out. I'll briefly explain some necessary concepts.

Concepts:
A wide definition is one that includes things that it should not. For example, defining a car as a vehicle is too wide because a bicycle is also a vehicle.

A narrow definition is one that fails to include things that it should. "Consider the definition of religion as any belief system that includes worshiping a god who created the universe. This definition is too narrow since it excludes religions that do not postulate a creator, such as Jainism and certain versions of Buddhism and Daoism."

A necessary condition is something that must be met first for something else to follow. It is necessary to have 4 sides to be a square. It is necessary to have HIV to develop AIDS.

A sufficient condition is one that implies the existence of something. Being a grandfather is sufficient for being a father as one must first be a father to become a grandfather.

All together now: Oxygen is necessary for life but not sufficient for it.

The exercise:
Suppose we have a definition X=Y. Are the following statements correct about this definition? Why or why not?

A) If the definition is too wide, then X is not necessary for Y.

B) If the definition is too wide, then Y is not necessary for X.

C) If the definition is too narrow, then X is not sufficient for Y.

D) If the definition is too narrow, then Y is not sufficient for X.

E) If X is not necessary for Y, then the definition is too wide.

Answers:
A) True
B) False
C) True
D) False
E) True

8000 years before Jesus, the Egyptian god Horus said, "I am the way, the truth, the life."
Find all posts by this user
Like Post Quote this message in a reply
16-03-2014, 07:45 AM
RE: Critical thinking exercise problem
That just did my head right in...

[img]

via GIPHY

[/img]
Visit this user's website Find all posts by this user
Like Post Quote this message in a reply
16-03-2014, 08:01 AM
RE: Critical thinking exercise problem
All those xs and ys look too much like math for my head. And it's early...I got nuthin'.

I'm not anti-social. I'm pro-solitude. Sleepy
Find all posts by this user
Like Post Quote this message in a reply
16-03-2014, 12:41 PM
RE: Critical thinking exercise problem
That's not a critical thinking exercise, it's a math exercise.

All of the examples given using definitions are moot; example: a car IS a vehicle, it's part of the vehicle group, words never mean one thing context must always be taken into account. Just because a bike is also a vehicle does not mean a car is not, the logic there is so faulty it's difficult to describe.

The same problem exists with the definition of religion, words do not contain a singular ultimate meaning, they're contextual and cultural relevance MUST be taken into account during usage, you can't look at linguistics in a purely analytic mind set, it by it's nature as a communication medium between different peoples requires the flexibility of things meaning different things to different people at different times and places.

The problem is the usage of the word define.
Find all posts by this user
Like Post Quote this message in a reply
16-03-2014, 05:56 PM
RE: Critical thinking exercise problem
This seems basic logic coated with complicated notation that probably would serve useful later on. But what do you need help with? you don't undertand those concepts?

[Image: sigvacachica.png]
Find all posts by this user
Like Post Quote this message in a reply
16-03-2014, 07:29 PM
RE: Critical thinking exercise problem
(16-03-2014 05:56 PM)nach_in Wrote:  This seems basic logic coated with complicated notation that probably would serve useful later on. But what do you need help with? you don't undertand those concepts?

I understand the concepts but I'm struggling with the abstract nature of how it's put. I need an example of someones train of thought in dealing with abstract exercises like this.

8000 years before Jesus, the Egyptian god Horus said, "I am the way, the truth, the life."
Find all posts by this user
Like Post Quote this message in a reply
16-03-2014, 07:50 PM
RE: Critical thinking exercise problem
(16-03-2014 12:41 PM)Sceadwian Wrote:  That's not a critical thinking exercise, it's a math exercise.

No it's not. It's a critical thinking exercise. Critical thinking is composed of many elements. The whole purpose is to get clarity and objectivity in one's thinking using a vast tool set. An example of such things is increasing one's sensitivity to literal meaning. Being able to assess whether a given definition is reportive, stipulative or precising not to mention too wide and/or too narrow. Logic and reason are fundamental principles in the study and maths is logic so you're close but you don't get your cigar. Using letters to represent variables is common in maths but it doesn't only happen in maths.

(16-03-2014 12:41 PM)Sceadwian Wrote:  All of the examples given using definitions are moot; example: a car IS a vehicle, it's part of the vehicle group, words never mean one thing context must always be taken into account. Just because a bike is also a vehicle does not mean a car is not, the logic there is so faulty it's difficult to describe.

The same problem exists with the definition of religion, words do not contain a singular ultimate meaning, they're contextual and cultural relevance MUST be taken into account during usage, you can't look at linguistics in a purely analytic mind set, it by it's nature as a communication medium between different peoples requires the flexibility of things meaning different things to different people at different times and places.

The problem is the usage of the word define.

In order to convey more clearly the intrinsic aspects of a concept, it is useful to employ extremes to highlight them.

8000 years before Jesus, the Egyptian god Horus said, "I am the way, the truth, the life."
Find all posts by this user
Like Post Quote this message in a reply
16-03-2014, 08:22 PM
RE: Critical thinking exercise problem
When dealing with these stuff I just try to explain things in my head with more words until I get that clarity moment. Trying not to use examples as they tend to be dangerous when using logic.

So, A) for example: When a definition is too wide it means you won't always get what you need, the set is too big and contains more than it should (hence the car/bicycle example). So if Y (the definition) is too wide, then you could get Y without X, because X is a smaller subset of Y.
For B) the things get the other way around, thus it gets the opposite answer. If X is a subset of Y, you can't get to X outside Y, so Y IS necessary for X.

Sufficient is not the opposite of necessary, don't make that mistake, they're two different things that work together.
So for C) you get that Y is smaller than X, it's contained in X, so not every X implies Y, you'd need more conditions to reach Y, so X is not enough for Y.
For D), while you can't get to Y from X you can't avoid X from Y, you won't get every X (because the definition is narrow) but you'll always imply X.


There's a nice example for sufficient conditions (in this case it's worth it): "Sally always uses an umbrella when it's raining". That means that rain is a sufficient condition for Sally using an umbrella, but she could use it in some other situation.

So if it rains (Y) Sally will use the umbrella (X) -> D).
But if she uses an umbrella (X) you can't know if it's raining or not (Y) ->C)

E) It seems the same as A) but it's the other way around, but the reasoning is simillar to A). If you can get to Y without X then X is either smaller (like in A)) or outside Y (unlike A)). Either way the definition is too wide, as it includes things that should not (ie. more or different than X)


Hope it helped... these things usually need a lot of effort to get the first few times and then it just becomes natural, so keep thinking Wink

[Image: sigvacachica.png]
Find all posts by this user
Like Post Quote this message in a reply
28-03-2014, 08:09 AM
RE: Critical thinking exercise problem
(16-03-2014 08:22 PM)nach_in Wrote:  When dealing with these stuff I just try to explain things in my head with more words until I get that clarity moment. Trying not to use examples as they tend to be dangerous when using logic.

So, A) for example: When a definition is too wide it means you won't always get what you need, the set is too big and contains more than it should (hence the car/bicycle example). So if Y (the definition) is too wide, then you could get Y without X, because X is a smaller subset of Y.
For B) the things get the other way around, thus it gets the opposite answer. If X is a subset of Y, you can't get to X outside Y, so Y IS necessary for X.

Sufficient is not the opposite of necessary, don't make that mistake, they're two different things that work together.
So for C) you get that Y is smaller than X, it's contained in X, so not every X implies Y, you'd need more conditions to reach Y, so X is not enough for Y.
For D), while you can't get to Y from X you can't avoid X from Y, you won't get every X (because the definition is narrow) but you'll always imply X.


There's a nice example for sufficient conditions (in this case it's worth it): "Sally always uses an umbrella when it's raining". That means that rain is a sufficient condition for Sally using an umbrella, but she could use it in some other situation.

So if it rains (Y) Sally will use the umbrella (X) -> D).
But if she uses an umbrella (X) you can't know if it's raining or not (Y) ->C)

E) It seems the same as A) but it's the other way around, but the reasoning is simillar to A). If you can get to Y without X then X is either smaller (like in A)) or outside Y (unlike A)). Either way the definition is too wide, as it includes things that should not (ie. more or different than X)


Hope it helped... these things usually need a lot of effort to get the first few times and then it just becomes natural, so keep thinking Wink

Erm, it's pretty damn rude of me to take this long to reply in thanks to your much appreciated help. Thank you very much!! I understand what's going on. I have similar problems when dealing with abstract issues. I'm just never quite sure how to put them in my head.

You rock man!Bowing

8000 years before Jesus, the Egyptian god Horus said, "I am the way, the truth, the life."
Find all posts by this user
Like Post Quote this message in a reply
Post Reply
Forum Jump: