MHB Is the Validity of an Argument Dependent on Premise Truth?

[solakis1]

it has been claimed that in an argument false premises can never produce a correct conclusion.is that correct ??

 

[Evgeny.Makarov]

"An argument" is not a term that is used in most textbooks of mathematical logic. What Copi calls a valid or invalid argument is a true (correspondingly, false) claim about logical (or semantic) consequence. This claim is usually denoted by $\Gamma\models A$ where $\Gamma$ is a set of formulas and $A$ is another formula.

That said, a valid argument with false premises can definitely have a true conclusion. For example, $p\land\neg p\models q\to q$ is a valid argument (form).

 

[HallsofIvy]

If tomorrow is Christmas then 2+ 2= 4.

 

[solakis1]

"An argument" is not a term that is used in most textbooks of mathematical logic. What Copi calls a valid or invalid argument is a true (correspondingly, false) claim about logical (or semantic) consequence. This claim is usually denoted by $\Gamma\models A$ where $\Gamma$ is a set of formulas and $A$ is another formula.

That said, a valid argument with false premises can definitely have a true conclusion. For example, $p\land\neg p\models q\to q$ is a valid argument (form).

Is the following argument valid?
1)if 2+2=4,then 3+6=5.......false
2) 2+2 is not 4..........false
conclusion: 3+6 is not 5........true
Here we also have false premises implying true conclusion

 

[Evgeny.Makarov]

Since the term "argument" is not usually used in books on mathematical logic, as I wrote above, I am not familiar with the definition of a valid argument when it involves digits, + and =. If the statements occurring in an argument are proposition or predicate formulas that consist of some generic propositional variables, functionl and predicate symbols, then I believe I know the definition, but not when formulas have symbols that usually have a fixed meaning.

 

[solakis1]

Since the term "argument" is not usually used in books on mathematical logic, as I wrote above, I am not familiar with the definition of a valid argument when it involves digits, + and =. If the statements occurring in an argument are proposition or predicate formulas that consist of some generic propositional variables, functionl and predicate symbols, then I believe I know the definition, but not when formulas have symbols that usually have a fixed meaning.

okay let me get rid of the +,=

1) if London is in England ,then Paris is in Gernany......false
2) but London is not in England...............false
conclusion: hence Paris is not in Gernany...........true
Is that argument valid?
That is propositional calculus
London is in England is a proposition which is true
Paris is in Gernany is also a proposition which false
Hence Paris in not in Germany is proposition which is true
London is not in England is a proposition which is false

 

[Evgeny.Makarov]

Instead of writing another example it would be more useful to provide a definition of a valid argument.

If the statements occurring in an argument are proposition or predicate formulas that consist of some generic propositional variables, functional and predicate symbols, then I believe I know the definition, but not when formulas have symbols that usually have a fixed meaning.

Your argument involves not just propositional variables, but propositional constants (such as "London is in England"), which have fixed truth values.

 

[solakis1]

i did write on my post No 6 that the argument form corresponding to the argument mentioned is the formula ((p->q)$~p)->~q) where p,q are variables and the above argument is just an instant subsitution of this formula.
But i don't know why that disappeared from my post No 6

 

[Evgeny.Makarov]

The argument that derives $\neg q$ from $p\to q$ and $\neg p$ is not valid. You most likely already know this.

 

[solakis1]

OK

The argument that derives $\neg q$ from $p\to q$ and $\neg p$ is not valid. You most likely already know this.

OK and one of the substitution instances of this argument form is my argument in post No 6
And i ask you again is the argument in that post valid?

 

[Evgeny.Makarov]

And i ask you again is the argument in that post valid?

And I am telling you again:

If the statements occurring in an argument are proposition or predicate formulas that consist of some generic propositional variables, functional and predicate symbols, then I believe I know the definition, but not when formulas have symbols that usually have a fixed meaning.

And knowing your tendency to conceal the definitions you use, I expect you to ask this question several more times without revealing the definition or the reason for your question.