Arithmetic and tautology

[iolo]

You have provided a single statement, "three plus four equals seven".

A tautology would be something like:
3+4=7, therefore 3+4=7.

The following two are tautologous :-

There are 7 days in a week
There are (3+4) days in a week.

Here's two tautologies :-

If you have (3+4) apples, then you also have 7 apples
If you have (3+4) bananas then you have (4+3) bananas.

Isn't a tautology saying the same thing in two different ways?

3+4=7, therefore 3+4=7 is an identity.

Surely a tautology is something obvious that someone might choose to deny, like 'Right-wingers are liars'. 5 + 2 = 7 is something even they wouldn't deny, so it is a (provisional) fact. A cliché is something that is too obvious to be worth stating:

My cat
does sit
upon a mat.

 

[untermensche]

The two sides are not equal logically.

They are only equal by definition.

4 = 4 is a logical equivalence however.

A thing is logically equivalent to itself. A meaningless tautology.

How do you apply these definitions without logic?

An example of an operation would be: When you get to the intersection turn left.

What logic is applied in turning left? It is just following an order.

 

[Speakpigeon]

How do you apply these definitions without logic?

An example of an operation would be: When you get to the intersection turn left.

What logic is applied in turning left? It is just following an order.

I still don't understand Juma's question.

That you need logic to apply definitions in arithmetics is part of arithmetic being a logical system. However, that doesn't make a statement like "3 + 4 = 7" a tautology since the proposition "3 + 4 = 7" is not always true. "3 + 4 = 7" is not necessarily true if you don't include all assumptions, and arithmetical definitions in particular, in your statement. Without those, 3 + 4 = 10 in base 7 for example and 11 in base 6.
EB

 

[untermensche]

An example of an operation would be: When you get to the intersection turn left.

What logic is applied in turning left? It is just following an order.

I still don't understand Juma's question.

That you need logic to apply definitions in arithmetics is part of arithmetic being a logical system. However, that doesn't make a statement like "3 + 4 = 7" a tautology since the proposition "3 + 4 = 7" is not always true. "3 + 4 = 7" is not necessarily true if you don't include all assumptions, and arithmetical definitions in particular, in your statement. Without those, 3 + 4 = 10 in base 7 for example and 11 in base 6.
EB

I don't understand it either.

A mathematical operation is an order to do something.

It isn't logic.

 

[Juma]

An example of an operation would be: When you get to the intersection turn left.

What logic is applied in turning left? It is just following an order.

I still don't understand Juma's question.

That you need logic to apply definitions in arithmetics is part of arithmetic being a logical system. However, that doesn't make a statement like "3 + 4 = 7" a tautology since the proposition "3 + 4 = 7" is not always true. "3 + 4 = 7" is not necessarily true if you don't include all assumptions, and arithmetical definitions in particular, in your statement. Without those, 3 + 4 = 10 in base 7 for example and 11 in base 6.
EB

Obviously that is implicated since 7 is not represented that way in base 7.
Yeez. That the use of suitable definitions is implied is a nobrainer.

 

[Juma]

I still don't understand Juma's question.

That you need logic to apply definitions in arithmetics is part of arithmetic being a logical system. However, that doesn't make a statement like "3 + 4 = 7" a tautology since the proposition "3 + 4 = 7" is not always true. "3 + 4 = 7" is not necessarily true if you don't include all assumptions, and arithmetical definitions in particular, in your statement. Without those, 3 + 4 = 10 in base 7 for example and 11 in base 6.
EB

I don't understand it either.

A mathematical operation is an order to do something.

It isn't logic.

Yes it is, see Speakpidgeons answer.

 

[untermensche]

I don't understand it either.

A mathematical operation is an order to do something.

It isn't logic.

Yes it is, see Speakpidgeons answer.

A "+" sign is just an order to perform a specific function.

That is not logic any more than some mother telling their child to go to bed is logic.

 

[Juma]

Yes it is, see Speakpidgeons answer.

A "+" sign is just an order to perform a specific function.

That is not logic any more than some mother telling their child to go to bed is logic.

Algebra is an axiomatic system. Not a collection of IKEA building instructions.

 

[untermensche]

A "+" sign is just an order to perform a specific function.

That is not logic any more than some mother telling their child to go to bed is logic.

Algebra is an axiomatic system. Not a collection of IKEA building instructions.

Non-sequitur.

 

[Juma]

Algebra is an axiomatic system. Not a collection of IKEA building instructions.

Non-sequitur.

Quoting Ingemark Stenmark: "dä int lönt å förklar för den som int begrip". (it aint worth explaining for who doesnt get it)

 

[untermensche]

Non-sequitur.

Quoting Ingemark Stenmark: "dä int lönt å förklar för den som int begrip". (it aint worth explaining for who doesnt get it)

In English that is called a cop out.

 

[Speakpigeon]

I still don't understand Juma's question.

That you need logic to apply definitions in arithmetics is part of arithmetic being a logical system. However, that doesn't make a statement like "3 + 4 = 7" a tautology since the proposition "3 + 4 = 7" is not always true. "3 + 4 = 7" is not necessarily true if you don't include all assumptions, and arithmetical definitions in particular, in your statement. Without those, 3 + 4 = 10 in base 7 for example and 11 in base 6.
EB

Obviously that is implicated since 7 is not represented that way in base 7.
Yeez. That the use of suitable definitions is implied is a nobrainer.

You're confusing logic and linguistic practice.

The question was whether 3 + 4 = 7 is a tautology, not whether we see how it can be construed as being true.
EB