My Math Forum  

Go Back   My Math Forum > College Math Forum > Applied Math

Applied Math Applied Math Forum


Reply
 
LinkBack Thread Tools Display Modes
August 24th, 2015, 02:31 PM   #1
Newbie
 
Joined: Aug 2015
From: Isengard

Posts: 7
Thanks: 0

“No head injury is too trivial to ignore”

Hi,

I was studying logic and mathematical thinking and I came across this sentence that has been puzzling me for a while:

“No head injury is too trivial to ignore”.

Apparently the sentence has a unintended meaning which makes it a nonsensical expression.

I am trying to figure out what the flaw is and I came up with the following example:

“This couch is too big to fit in the house”.

Which I believe it can be re-written as “the couch is so big that it does not fit in the house”.

On the contrary if I were to say, "no couch is too big to fit in the house" I think is equivalent to "no couch is so big that it does not fit in the house", which essentially means "all the couches, even big ones, fit in the house". (Please correct me if I'm wrong).

Based on this logic saying "no head injury is too trivial to ignore" which can be re-written as "no head injury is so trivial that it should not be ignored". I don't even know if I understand what this means. If this was the case can we do something like the situation with the couch in the house?

I would really appreciate if someone could explain this in clear manner with details and using predicate logic if necessary.
mick17 is offline  
 
August 24th, 2015, 03:14 PM   #2
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,091
Thanks: 2360

Math Focus: Mainly analysis and algebra
Quote:
Originally Posted by mick17 View Post
re-written as "no head injury is so trivial that it should not be ignored"
I think you have an error. The second "not" is incorrect.

One possible reason for your error is that the original is an implicit "not less than" relation, while your example is an implicit "not greater than" relation.

Last edited by v8archie; August 24th, 2015 at 03:22 PM.
v8archie is offline  
August 24th, 2015, 03:32 PM   #3
Newbie
 
Joined: Aug 2015
From: Isengard

Posts: 7
Thanks: 0

Quote:
Originally Posted by v8archie View Post
I think you have an error. The second "not" is incorrect.

One possible reason for your error is that the original is an implicit "not less than" relation, while your example is an implicit "not greater than" relation.
Thanks for your answer.
Can you expand a a little bit on what you mean?
mick17 is offline  
August 24th, 2015, 04:14 PM   #4
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 2,876
Thanks: 766

As what is wrong with the sentence, is that it is saying that, because no head injury is trivial, they can all be ignored!

"No head injury is too trivial to be ignored"
Country Boy is offline  
August 25th, 2015, 09:39 AM   #5
Newbie
 
Joined: Aug 2015
From: Isengard

Posts: 7
Thanks: 0

Quote:
Originally Posted by Country Boy View Post
As what is wrong with the sentence, is that it is saying that, because no head injury is trivial, they can all be ignored!

"No head injury is too trivial to be ignored"
Can you explain as if I were a 10 year old kid how you came to that conclusion? I mean in a more fundamental sense.

I don't get why you interpret "because no head injury is trivial" then "they can all be ignored!". What makes you think there is an implication there? What are the consequences of having that "too" in the sentence?

I know there is a flaw in the sentence but the reason is quite unclear to me.
mick17 is offline  
August 25th, 2015, 11:12 AM   #6
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 2,876
Thanks: 766

Quote:
Originally Posted by mick17 View Post
Can you explain as if I were a 10 year old kid how you came to that conclusion? I mean in a more fundamental sense.

I don't get why you interpret "because no head injury is trivial" then "they can all be ignored!". What makes you think there is an implication there? What are the consequences of having that "too" in the sentence?

I know there is a flaw in the sentence but the reason is quite unclear to me.
Do you understand what "too trivial to be ignored" means? Can you explain your understanding of that portion of the sentence?
Country Boy is offline  
August 26th, 2015, 01:45 AM   #7
Newbie
 
Joined: Aug 2015
From: Isengard

Posts: 7
Thanks: 0

Quote:
Originally Posted by Country Boy View Post
Do you understand what "too trivial to be ignored" means? Can you explain your understanding of that portion of the sentence?
To me the kind of expression "Too x to y", where x is an adjective and y represents a verb (action) either in active or passive form, is the equivalent to "so x that it can't y".

So in this case I think "Too trivial to be ignored" means "so trivial that it can't be ignored".
mick17 is offline  
August 26th, 2015, 05:09 PM   #8
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 2,876
Thanks: 766

Quote:
Originally Posted by mick17 View Post
To me the kind of expression "Too x to y", where x is an adjective and y represents a verb (action) either in active or passive form, is the equivalent to "so x that it can't y".

So in this case I think "Too trivial to be ignored" means "so trivial that it can't be ignored".
Yes, which is what I said before, "because no head injury is trivial, they can all be ignored!"
Country Boy is offline  
August 27th, 2015, 12:58 PM   #9
Newbie
 
Joined: Aug 2015
From: Isengard

Posts: 7
Thanks: 0

Quote:
Originally Posted by Country Boy View Post
Yes, which is what I said before, "because no head injury is trivial, they can all be ignored!"
I don't think I understand the process behind your conclusion. But pondering about it I believe the confusion arises firstly when the negation is introduced in the sentence and secondly when we misunderstand the phrase "too trivial".

If

(1) "too trivial to be ignored"

means

(2) "so trivial that it cannot be ignored"

which per se is a semantic nonsense, then if we say

(3) "there are injuries that are too trivial to be ignored",

we would mean

(4) "There are head injuries that are so trivial that cannot be ignored".

If we introduce the negation

(5) "There does not exist any head injury too trivial to be ignored"

which based on (4) would be the same as

(6) "There does not exist any head injury which is so trivial that cannot be ignored"

extracting the negation of the quantifier of (6)

(7) "Every head injury, no matter how trivial, can be ignored"

This is because being $\displaystyle x$ a head injury and a predicate such that

$\displaystyle P(x) := $ "$\displaystyle x$ is so trivial that cannot be ignored"

$\displaystyle \nexists x. P(x) \iff \forall x. \neg (P(x))$

It is easier to think of it in a more generic way. For example:

"No WUG is too DAX to be ZONGED"

WUG can always be ZONGED, whether WUG is DAX or not. If we fill the sentence with real words such as:

"No football team is too good to be defeated"

This can be re-formulated as:

"Every football team, no matter how good, can be defeated"

Last edited by mick17; August 27th, 2015 at 01:06 PM. Reason: something missing
mick17 is offline  
August 30th, 2015, 07:55 AM   #10
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 2,876
Thanks: 766

Quote:
Originally Posted by mick17 View Post
"No football team is too good to be defeated"

This can be re-formulated as:

"Every football team, no matter how good, can be defeated"
Yes, and "No head injury is too trivial to be ignored" can be re-formulated, in exactly the same way, as:
"Every head injury, no matter how trivial, can be ignored".

It's basic English grammar.
Country Boy is offline  
Reply

  My Math Forum > College Math Forum > Applied Math

Tags
“no, fallacies, head, ignore”, injury, logic, mathematical logic, reasoning, thinking, trivial



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Head maths fruitymaths Elementary Math 10 December 1st, 2014 07:56 PM
Best way of multiplying numbers in head ? fruitymaths Elementary Math 13 October 9th, 2014 06:07 PM
Hello everyone, I am in over my head. cr12678 New Users 3 December 11th, 2011 12:01 PM
I'm scratching my head Larry Rudnicki Algebra 1 January 15th, 2008 11:54 PM





Copyright © 2017 My Math Forum. All rights reserved.