propositional calculus

[chrislav]

is the sentence: 7+3=1or paris is inFrance true or false and why?

 

[Dr.Peterson]

is the sentence: 7+3=1or paris is inFrance true or false and why?

Please tell us what you think the answer is, and why; then we'll have something to discuss.

I presume the sentence is this:

7+3=1 or Paris is in France​

The most important thing we'll discuss is how logical language differs from everyday language.

 

[chrislav]

what do you mean, ipresume

isnt my question clear

By definition in logic the above is true

AND the most important thing to discuss is why the above definition is as such and not the opposite
I mean the above sentence to be false since 7+3=1 is false

 

[blamocur]

By definition in logic the above is true

True

I mean the above sentence to be false since 7+3=1 is false

Do you know the truth table for the OR operator?

 

[chrislav]

True

Do you know the truth table for the OR operator?

yes I DO
and i am asking why the table of the OR operator considers the above sentence as true and not false

 

[mario99]

is the sentence: 7+3=1or paris is inFrance true or false

$7 + 3 = 1 \rightarrow \ \text{false}$
Paris is in France $\rightarrow \ \text{true}$

$\text{false} \ + \ \text{true} = \text{true}$

and why?

because the logical OR ( || ) operator is true if and only if one or more of its operands is true.

 

[chrislav]

$\text{false} \ + \ \text{true} = \text{true}$


.

false + true = false, if by the symbol (+) you mean the logical symbol (^)
Please read my post no 3

 

[fresh_42]

false + true = false, if by the symbol (+) you mean the logical symbol (^)
Please read my post no 3

No.

"false $+$ true" means "false $\vee$ true" means "false OR true" resulting in "true"
"false $\cdot$ true" means "false $\wedge$ true" means "false AND true" resulting in "false"

It is addition and multiplication modulo $2$ in $\mathbb{Z}_2=\{0,1\}$, i.e. $0+1=1$ and $0\cdot 1=0.$

Another way to see it is with Venn diagrams. $A\cup B$ means "in A OR in B", $A\cap B$ means "in A AND in B".

 

[chrislav]

ok ok but read and answer the last paragraph of my post no 3

 

[Dr.Peterson]

By definition in logic the above is true

AND the most important thing to discuss is why the above definition is as such and not the opposite
I mean the above sentence to be false since 7+3=1 is false

What sort of answer are you expecting?

The sentence "7+3=1 or Paris is in France" is true because at least one of its parts is true, which is what "or" means. That's been stated several times.

In contrast, the sentence "7+3=1 and Paris is in France" is false, because "and" requires that both parts be true.

If you think this is wrong, please explain why. (This is what I asked you to do initially.)

 

[fresh_42]

ok ok but read and answer the last paragraph of my post no 3

I'm not sure I understand.

AND the most important thing to discuss is why the above definition is as such and not the opposite
I mean the above sentence to be false since 7+3=1 is false

You did not use AND. You said ... (emphasis mine)

is the sentence: 7+3=1or paris is inFrance true or false and why?

... OR. The statement "7+3=1 and Paris is in France" is false. However, with an or where it reduces to "false or true" it is true. That's the difference between AND and OR, multiplication and addition, intersection and union.

 

[blamocur]

why the table of the OR operator considers the above sentence as true and not false

This is how OR is defined, is not it?

 

[chrislav]

This is how OR is defined, is not it?

yes it is .
But why ,OR, is defined so
For example in mathematics the sqrt it is defined in a certain way because there is a theorem of existence to justify the definition.
Here what is behind to justify such a definition
if i define the V as follows: TVT=T,TVF=F,FVT=F,FVF=F WHAT will happen

 

[Dr.Peterson]

if i define the V as follows: TVT=T,TVF=F,FVT=F,FVF=F WHAT will happen

Then you will have defined V ("OR") as a synonym of ∧ ("AND"), because this is the truth table for ∧.

Why would you choose to do that?

You'll still need a name/symbol for what we currently call V ("OR").

And your definition will bear no relationship with the English word "or", as the existing definition does. That relationship is the justification for the definition.

 

[chrislav]

you sure that if you ask anybody that has not been taught logic will know the answer that 7+3=1OR paris is in France is true or false ?
Try it
And if he says true and you say no is false,because 7+3=1 is false will refer you to the definition in logic,when he does not even know what logic is
So the relation to the english word ,OR, is not the justification

 

[topsquark]

you sure that if you ask anybody that has not been taught logic will know the answer that 7+3=1OR paris is in France is true or false ?
Try it
And if he says true and you say no is false,because 7+3=1 is false will refer you to the definition in logic,when he does not even know what logic is
So the relation to the english word ,OR, is not the justification

It doesn't matter if they've been taught logic or not. What matters is how Mathematician's define the OR operator, not how someone untrained reads it.

As another example of this kind of thing, if you ask most people what sign you get when you multiply a negative by a negative, many will respond negative, even if they've been taught otherwise (presumably years ago.)

When we (ie. the Mathematicians) define a term that definition has to hold, whether it makes sense to the average member of society. We could call the OR operator THINGAMABOB and your statement will now read
7 + 3 = 1 THINGAMABOB Paris is in France. The result will be true.

If you are arguing that the term needs to have it's name changed, you are far too late: it's too well entrenched.

-Dan

 

[fresh_42]

It doesn't matter if they've been taught logic or not. What matters is how Mathematician's define the OR operator, not how someone untrained reads it. ...

And as an additional side note: We are currently communicating on devices that heavily depend on the truth tables of AND and OR. They wouldn't function otherwise!

 

[chrislav]

It doesn't matter if they've been taught logic or not. What matters is how Mathematician's define the OR operator, not how someone untrained reads it.

The definition does not to belong to a mathematician and the evolution of logic to its present morphification is due to a particular book (the 1st book of logic in our planet ) writen by a particular philosopher

As another example of this kind of thing, if you ask most people what sign you get when you multiply a negative by a negative, many will respond negative, even if they've been taught otherwise (presumably years ago.)

and if they ask why you must say because of the theorem in real nos (-a)(-b)=ab .But here we have a theorem to justify our problem,whilst on the other hand we have a definition to justify.And thereis a great difference between a theorem and a definition

When we (ie. the Mathematicians) define a term that definition has to hold, whether it makes sense to the average member of society.

wrong. You mathematicians you must have a theorem of existence of a new concept before you define it.

If you are arguing that the term needs to have it's name changed, you are far too late: it's too well entrenched.

-Dan

 

[fresh_42]

wrong. You mathematicians you must have a theorem of existence of a new concept before you define it.

No, we don't. "The elements of the empty sets have purple eyes" is a true statement, even if senseless. E.g. we often use that every set can be well-ordered, but nobody knows a well-ordering of the real numbers. Definitions without instances usually drop out of usage and will be ignored, but there is no rule that requires an instance. However, in your case here: you are using an instance right now!

 

[topsquark]

wrong. You mathematicians you must have a theorem of existence of a new concept before you define it.

But it is defined! The only problem seems to be that you don't like what it's being called.

-Dan