Semantics Question #1, 2, 3, & 4 (Are these Right?)

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Reply Tue 24 Nov, 2009 03:18 pm
Hello. I am not going to pretend this isn't homework. This is the first of 5 questions that I have on Semantics, and I wonder if anyone can tell me if I am right on this first question.

I realize notation and sometimes vocabulary vary and so am not sure how understandable this is:


Find a formula of ψ such that ψ is not a sentence but contains part that is a sentence...


My answer: ∀xFx ∨ Gy


A sentence is "a formula that contains no free occurrence of a variable," and so I offer ∀xFx ∨ Gy as a formula because it is not a sentence (the "y" is free) , and it contains part that is a sentence (∀xFx).

Thanks in advance. And if your good at this stuff. Please follow the other four questions I will be working through.

____________

I'm adding another one.


If # = [Fx→[[∀xFx→Fx]→Fx]] and a=x and b=y, then what happens what #(a/b)


As I understand it, this means that all free occurrences of a will be replaced with the variable b.
So I recognize that ∀x binds all x's in its scope. There are 5 x's, and so I need to determine what the scope of ∀x is. Clearly the first x is outside the scope, but as for the other 4 I don't really see the last two falling within its scope in the same way that the 3rd one does.


So would I have: [Fy→[[∀xFx→Fy]→Fy]]


Am I right?
 
Horace phil
 
Reply Tue 24 Nov, 2009 03:27 pm
@Horace phil,
Hi. I need to find a formula of ψ such that ψ contains occurrences of a variable a that are bound and at least one occurrence of a that is free.


I would offer: ∀x[∃ y[Hy ∨ Gz] → Jxy]


As I see it the first two "y's" are bound, and the final one is not. See "y" as variable "a."

Am I understanding properly?

______________________
Edit: Turns out you can only open two threads per...
As a result I place another question here:




I need to find a sentence of such that contains no proper part that is a sentence but does contain at least one binary connective.


I would offer: ∀x(Fa ∨ Ga)


It seems to me that no sub-formula is closed, so its not a sentence, but does it contain at least one binary connective? I remember "v" as being a binary connective.


Am I understanding this properly?
 
Horace phil
 
Reply Sun 29 Nov, 2009 10:39 am
@Horace phil,
Any help people?
 
Emil
 
Reply Sun 29 Nov, 2009 06:09 pm
@Horace phil,
What about:

1. Do your own homework.
2. If you can't do it, then ask your teacher.

What's the point of having people here do your homework?
 
Theaetetus
 
Reply Sun 29 Nov, 2009 06:20 pm
@Horace phil,
There are ways to go about receiving help on homework on this forum indirectly, which none of us would really have a problem with. Telling everyone that you are not going to pretend this isn't homework is not one of them. Why not start a discussion on the concepts of your homework? Why not ask some basic general questions?

By listing a series of questions from your homework and asking everyone to do your work, you are attempting to plagiarize your work, and that could get you an F, suspended, or kicked school, since you would not be doing the work yourself.
 
Emil
 
Reply Sun 29 Nov, 2009 06:44 pm
@Theaetetus,
Theaetetus;106948 wrote:
There are ways to go about receiving help on homework on this forum indirectly, which none of us would really have a problem with. Telling everyone that you are not going to pretend this isn't homework is not one of them. Why not start a discussion on the concepts of your homework? Why not ask some basic general questions?

By listing a series of questions from your homework and asking everyone to do your work, you are attempting to plagiarize your work, and that could get you an F, suspended, or kicked school, since you would not be doing the work yourself.


It's entirely possible the teacher could find this thread on Google. Depending on how careful you are.
 
Horace phil
 
Reply Sun 29 Nov, 2009 09:35 pm
@Emil,
Here's what I don't get: Haven't I done the homework? After having done the homework I am now asking for some feedback. Have I done them properly? I think this is entirely within the grounds of acceptability. Don't you?
 
Theaetetus
 
Reply Mon 30 Nov, 2009 12:06 am
@Horace phil,
Well, when I used to be a math tutor, many of my students would come to me doing homework wrong, and then would basically expect me to go through with them how to get the right answers. Sure they did the work, but it was wrong, and they knew it. I am not saying that you are doing this, but based on experience that is what I have witnessed.

I honestly have no clue when it comes to logic. So I could not tell you whether what you did was right or wrong.
 
Horace phil
 
Reply Mon 30 Nov, 2009 07:11 am
@Theaetetus,
In my opinion I have come to individuals with what I believe are at least 4 questions done correctly. However, because there are people who know this stuff better than I do, I run it by them. This is entirely appropriate, and my having to justify myself is turning this into a waste of time.
 
 

 
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