LOGIC concepts

Ryan$

Junior Member
Joined
Jan 25, 2019
Messages
145
Hi guys ;
Can someone please illustrate me what does the word "only" mean in terms of math? I mean lets assume someone told me

"only motorcycles can enter this gate" so what should I understand from this? I'm really new on logic and frankly I'm not good as much as in math so please take that into consideration and I know all person has its own ability of understanding/learning.

thanks
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,784
Hi guys ;
Can someone please illustrate me what does the word "only" mean in terms of math? I mean lets assume someone told me

"only motorcycles can enter this gate" so what should I understand from this? I'm really new on logic and frankly I'm not good as much as in math so please take that into consideration and I know all person has its own ability of understanding/learning.

thanks
You can gain some understanding by moving it.

"only motorcycles can enter this gate"
"motorcycles only can enter this gate"
"motorcycles can only enter this gate"
"motorcycles can enter only this gate"
"motorcycles can enter this only gate"
"motorcycles can enter this gate only"

Which ones don't make sense? What should you not be modifying?

How does the meaning change with each one that does make sense?
 

pka

Elite Member
Joined
Jan 29, 2005
Messages
7,813
Hi guys ;
Can someone please illustrate me what does the word "only" mean in terms of math? I mean lets assume someone told me
"only motorcycles can enter this gate" so what should I understand from this? I'm really new on logic and frankly I'm not good as much as in math so please take that into consideration and I know all person has its own ability of understanding/learning.
Ryan$, 'only' is not a mathematical nor a logical term in and of itself.
The construction only if, has an important role to play in logic. Consider the sentence: "One may enter by way of this gate only if he/she is riding a motorcycle." That sentence means that if George enters by this gate then he does so riding his motorbike. The rule is: P only if Q is equivalent If P then Q.
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
3,039
Can someone please illustrate me what does the word "only" mean in terms of math? I mean lets assume someone told me

"only motorcycles can enter this gate" so what should I understand from this? I'm really new on logic and frankly I'm not good as much as in math so please take that into consideration and I know all person has its own ability of understanding/learning.
This is as much English as math. You have to think about what logical statement has the same meaning.

You will be writing something like "If _____, then _____". What has to go in each blank in order to mean "Only motorcycles can enter this gate"?

If this is a problem you were assigned, it may be helpful to look at answers given to similar examples or exercises, to see what form is expected; please show them to us, so we can be sure we are leading you in the right direction!
 

Jomo

Elite Member
Joined
Dec 30, 2014
Messages
3,005
Ryan$, 'only' is not a mathematical nor a logical term in and of itself.
The construction only if, has an important role to play in logic. Consider the sentence: "One may enter by way of this gate only if he/she is riding a motorcycle." That sentence means that if George enters by this gate then he does so riding his motorbike. The rule is: P only if Q is equivalent If P then Q.
Prof, can you please explain in a bit more detail why only motorcycles can enter this gate, is not the same as if you enter the gate, then you are on a motorcycle? Thanks for your time.
 

pka

Elite Member
Joined
Jan 29, 2005
Messages
7,813
Prof, can you please explain in a bit more detail why only motorcycles can enter this gate, is not the same as if you enter the gate, then you are on a motorcycle? Thanks for your time.
If P then Q.
P only if Q
P is sufficient for Q
Q is necessary for P
If not Q then not P.
All of those are equivalent to one another.

If one enters this gate then it in on a motor bike.
One enters this gate only if on a motor bike.
Entering this gate is sufficient for being on a motor bike.
Being on a motor bike is necessary for entering by this gate.
If one is not on a motor bike then one is not entering by this gate.
 

Ryan$

Junior Member
Joined
Jan 25, 2019
Messages
145
thanks to you all, I got the point behind!
 
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