# Does a+b=c?

jack phil

Wed 9 Jun, 2010 11:38 am
@jack phil,
Heh, I don't secretly know the answer to this question. As far as I can tell it is nonsense. I was wondering what my esteemed philosophers of logic might say.

But if a+b=c is nonsense, does that imply that 1+2=3 and 2+3=6 are also nonsense?

Mark Noble did note that the variables need not be numbers, so RED + CIRCLE = REDCIRCLE could be kindred to the mathematical assumptions being made. Or maybe someone else can think of another example.

In a certain way, the question that a+b=c is more of a logical one than a mathematical one. Man + Woman = Couple[sic]?

And on the track of Emil and Fast, can I look at a shade of RED and then calculate a color that is ~RED? Maybe different shades of not red? ...

For instance, I drew a mural on my friends' dry erase board, titled The Last Birfday, in which all of my friends sat around a table much like the Last Supper, and I'm with an oversized gut, lay across the table, passed out, with a beer in hand. Of course, reality is a bit different. They seemed to have liked the picture, maybe because I put some effort into it, maybe because it presented them like ~apostles, I really don't know. But maybe that is an example of painting (~)?

(Again, I don't really have an answer to this question; I am not sure if I am looking for a question without answer or truly seeking an answer; I might just be sharing the vision of a blind man; but this thread will take itself where it wants. Thankfully it is easy to follow!)

I hope I did not throw a wrench in the gears of this thread. Thanks to everyone for te great number of responses so far.

fast

Wed 9 Jun, 2010 11:42 am
@mark noble,
[QUOTE=mark noble;175055]If there are no values then, what must the values be?[/QUOTE]Just to be clear, I didn't say that there are no values for the variables given. There may very well be, but if there are (which I highly doubt, in case you're curious), we (that would be you and I) do not know what they are, for they have not been disclosed (to us). I suspect that the variables in the equation have no values at all since the equation was written here on this forum for the purpose of trying to make some philosophical point-whatever that might be.

I don't know what to make of your question. I see two oddities about it. First, even if the variables did have values, it wouldn't be the case that they must. Secondly, to ask what must the values be when there are no values is like asking why must it be so that there is cat on the table when there is no cat on the table. What kind of assumptive question is that? If there is no cat on the table, then it's not so that it must be on the table. It's not even the case that it is on the table!

[quote]Why are you using an archaic text style?[/QUOTE]It's a copy and paste issue, and hopefully the change in forums will resolve the issue. I've been doing better though. Emil hasn't gotten on me in a while about it.[/SIZE]

[quote]What does this mean "~L and L~"? It's just capital l's with eyebrows to me. [/QUOTE]That was my way of trying to point out the difference between "not like" and "like not." That latter implies the former, but the former doesn't imply that latter. However, this is a losing battle, for as Emil points out, "don't like" and "dislike" are also ambiguous between them both.[/SIZE]

It's probably easier to give another example. Some believe that an atheist is one that lacks belief that there is a God ~B(G). Notice that I placed the tilde behind the B. Hence, Allen the atheist does not have a belief that God exists.

Others believe that an atheist is one that believes there is no God (or that no God exists) B(~G). Bob the atheist (unlike Allen the atheist) does have a belief.

So, think of the difference between ~B and B~ as being the difference between "not belief" and "belief not." Allen (that has no belief) versus Bob (that does have a belief). Allen has no belief that God exists ~B(G), and Bob has a belief that God does not exist B(~G).

Do I like the members of the forum we're about to merge with? Well, I neither like them nor dislike them; I don't even know them! Well, I might, but you get the picture. There is a difference between not liking and liking not. ~L vs L~

The problem is "I don't like you" is ambiguous between ~L and L~, and if that isn't enough to be confused over, "I dislike you" is also ambiguous between ~L and L~.

I had gotten the impression that you thought that I didn't like you, and I interpreted you to mean L~, (even though I realized you could have meant ~L), so I just made it clear that I didn't L~, and I also made it clear that none of that was to say ~L either.

Then, you began to question even that, and here we finally wind up.

[quote]Why are you so fussed about me wishing you well, but have no qualms in doing so to me?[/QUOTE]I live in a glass house, and you don't, so I should mind that you would throw stones while I can completely ignore the fact I do. [/SIZE]

[quote]Mark...[/QUOTE]Could you at least put a space between the 'k' and first period? Then, you can take out the second period, the first period, the space between the 'k' and first period (yes, undo what you've just done). Then, once you knock out the third period, you've halfway done. All that's left then is to omit the name. [/SIZE]

Do you not think we're smart enough to know who is posting? Sure, sign your name once in a while if ya like (I've done it); be strange, but be strange in moderation. It's not just odd (but a bit too odd) to sign your name every single post, and my mild prodding is only for the purpose of reminding you of that. That's the real underlying reason for why I said "Hi Mark" at the end of my post, and it goes to shed some light on why I come across as I do when you repeatedly wish me well.

Brings smiles upon the faces of those you can,

fast

mark noble

Wed 9 Jun, 2010 12:24 pm
@fast,
Hi Fast,
But I haven't got a cat!

????...

Emil

Wed 9 Jun, 2010 12:29 pm
@jack phil,
Fast wrote:
That was my way of trying to point out the difference between "not like" and "like not." That latter implies the former, but the former doesn't imply that latter. However, this is a losing battle, for as Emil points out, "don't like" and "dislike" are also ambiguous between them both.

Actually, this is not the case. I know a person that I both dislike, hate even, and like, even love at the same time.

Fast wrote:
I've been doing better though. Emil hasn't gotten on me in a while about it.

I lost my patience for a while. I don't feel like doing a long guide to fix it for you, it's not that annoying. :p

fast

Wed 9 Jun, 2010 12:36 pm
@Emil,
Emil;175110 wrote:
I don't feel like doing a long guide to fix it for you, it's not that annoying. :p
Comma splice.

.......

---------- Post added 06-09-2010 at 02:41 PM ----------

mark noble;175108 wrote:
Hi Fast,
But I haven't got a cat!

????...

Yeah, that's what an atheist said after he stopped complaining of his hunger.

mister kitten

Wed 9 Jun, 2010 12:52 pm
@Owen phil,
Owen;175054 wrote:

We assume that (a+b_=c) is a mathematical question, because of the + and =. What things, other than numbers, could (a, b, c) be?

I didn't assume that it was a mathematical question. Variables can be whatever.
a + b = c
apple + banana = coconut
or
gorilla + cat = goat

fast

Wed 9 Jun, 2010 01:10 pm
@mister kitten,
[QUOTE=mister kitten;175121]I didn't assume that it was a mathematical question. Variables can be whatever.
a + b = c
apple + banana = coconut
[/QUOTE]

Let's not confuse our ability to use a letter to 1) denote (or stand in place of) an object and 2) denote a quantity of objects.

We learn to define variables. 'a' for instance can be defined as the number of apples.

Equation: a + b = c

Variables:

a = number of apples in the truck
b = number of banana's on the ground
c = number of coconuts that should be bought

If how many coconuts should be bought can be determined by the equation, then knowing the number of apples in the truck and banana's on the ground and the equation will help inform us of how many coconuts should be bought.

If we know the number of apples in the truck, then the value is known, but if we confuse 1 with 2 and think that 'a' simply stands in place for apples, then there can be no value of 'a'.

mark noble

Wed 9 Jun, 2010 01:17 pm
@fast,
Hi All,
This is how I worked it out.
a = 0 for it has no value, b = 0 for it has no value, 0+0=0 for c has no value. If no values are applied, the value is 0.
That was easy, wasn't it?
Have a really fantastic day, all.
Mark... (please forgive me fast, for I cannot not be me).

fast

Wed 9 Jun, 2010 01:20 pm
@mark noble,
mark noble;175131 wrote:
Hi All,
This is how I worked it out.
a = 0 for it has no value, b = 0 for it has no value, 0+0=0 for c has no value. If no values are applied, the value is 0.
That was easy, wasn't it?
Have a really fantastic day, all.
Mark... (please forgive me fast, for I cannot not be me).

Having no value and having a value of 0 is not the same thing.

ETA: there are exceptions, but this isn't one of them.

mark noble

Thu 10 Jun, 2010 10:04 am
Hi Fast,
Have you made it through the digital wormhole yet?
What are the default values of something that has no values?
If there are none, do you think we should set a precident?
Mark...

Thu 10 Jun, 2010 11:12 am
@jack phil,
jack phil wrote:
Does a+b=c?

Only for some values of a, b, and c.

MJA

Thu 10 Jun, 2010 11:23 am
@jack phil,

B?

And if A = B, and B = C, then A = C
They all look different to me, so what is truth,
What can it B?
Different or equal?
What should it B?
To B or not to B?
That is the question.
The Nature of B,
Aristotle, Shakespeare and Me.

=
MJA

Owen phil

Thu 10 Jun, 2010 12:12 pm
Agreed. If (a, b, and c) refer to numbers then ..

(2+3=5) implies, there are some numbers (a, b, and c) such that (a+b=c).
(2+3=5) is true.
therefore,
There are some numbers (a, b, and c) such that (a+b=c), is true.

Thu 10 Jun, 2010 12:22 pm
@jack phil,
jack phil wrote:

Does a+b=c?

Is it any more correct to say true rather than false?

Is this a nonsense question?

The question is impossible to answer based on facts given. It has the same basis as being asked, "Is the cat black?"

Without knowing which cat or what a, b and c are, there is no way to answer the questions.

triclino

Thu 18 Aug, 2011 06:48 pm
@jack phil,
jack phil wrote:

This is sort of an offshoot of the "this sentence is false thread". I think the solution to this question might be simpler than the solution to that one, which of course, may have the same solution as whether the chicken or egg came first.

Does a+b=c?

Is it any more correct to say true rather than false?

Is this a nonsense question?

?

I don't really know where to start, so I hope others will.

The exact expression is :

For all a, and for all ,b there exists a unique ,c such that : a+b = c.

And this expression can be proved in the following way :

1) for all ,x (x=x).........................................................................an axiom in equality

2) a+b = a+b ................................................................................from 1 and using Universal Elimination where we put : x = a+b

3) there exists ,c ( a+b =c) .............................................................from 2 and using Existential Introduction

Now for the uniqueness part:

4) a+b =c & a+b = d ..........................................................................Assumption to start a conditional proof.

5) c=d....................................................................From 4 and using the properties of the equality : for all ,x,y,z [ (x=y and y=z) => y=z] and also ,for all x,y ( x=y <=> y=x)

6) [(a+b=c )& (a+b=d) => c=d]....................................from 4 to 5 and using conditional proof

7) for all c,d [ (a+b=c)&(a+b=d) => c=d].......................................from 6 and using Universal Introduction

8)There exists a unique ,c( a+b=c) ..................................................from 3 and 7 and using the definition of uniqueness

9) for all a,b there exists a unique c (a+b=c)......................................by generalization of 8

This innocent little theorem allows mathematicians to do all sorts of substitutions like :

a+b+c+d =x................. x^4+ y^2 +c = w.........-((-x) + abc^2 + 1/x) =y e.t.c

Without that possible substitution ,perhaps, we would not have mathematics at all

Of course if you ask a mathematician what theorem or axiom whatsoever allows him/her to do such a substitution you will get all shorts of nonsenses .