A Cuestion on formal fallacies

[Leo Duluc]

I came a cross this formal fallacie:

If today is Saturday then tomorrow is Sunday.
Is not Saturday.

Tomorrow is no Sunday.

I understand that the structure of the argument is not valid (denying the antecedent). But in this case to give this as an example is hard to absorb the idea that there trying to convinced you of( At least a think that) that this is a invalid form of an arguement.

I would like to know your opinions.

Thank you.

 

[guten]

I don't know what their point is. It is hard to expect someone working with logical fallacies, doesn't know the relationship the days of the week have with each other. We know by our use of these terms that,

(1) If today is Saturday, then tomorrow is Sunday.
(2) If tomorrow is Sunday, then today is Saturday.

If we are then given that,

(3) Today is not Saturday.

We can not validly infer (no rule justifies the move) from (1) and (3) that

(4) Tomorrow is not Sunday.

But we can validly infer (4) from (2) and (3).

Given (3), we can pick any other day as an example of what day it is. Say we pick Monday. Then we know that tomorrow is Tuesday, which is not Sunday, which agrees with (4). But they tell you that this is fallacious, somehow expecting a person to not make the connection intuitively? I agree it is a poor example. They should not have used a conditional for which its converse is also true. That is confusing.

 

[HallsofIvy]

The point is that it is the structure of the argument that determines whether it is valid or not, not the truth or falsity of the specific statements using specific definitions for the words.

The structure of the argument, as given, is
If A then B
A is not true

Therefore B is not true.

That is invalid because it is possible to assign values to A and B that make the conclusion false. For example, let A= "It is raining", B= "I will drive to work". The argument becomes
If it is raining then I will drive to work
It is not raining

Therefore I will not drive to work.

That's wrong- I drive to work every day, whether it is raining or not (So the statement "If it is raining I will drive to work" is true) because I live to far from my job not to.

Here, it happens that the conclusion is true, but the argument- the structure- is invalid. It happens that the conclusion is true because, in fact, "Today is Saturday if and only if tomorrow is Sunday". That is, as guten said, both 1) "If today is Saturday then tomorrow is Sunday" and 2) "If tomorrow is Sunday then today is Saturday" are true.

A valid argument would be:
If tomorrow is Sunday, then today is Saturday
It is not Saturday

Therefore tomorrow is not Sunday

because it is of the form "If A then B", "not B", "therefore, not A"
and the "contrapositive" of "If A then B", "I not B then not A" is true.

 

[ssd]

Visualizing through sets:
If 'A' then 'B'.
But for an element 'b' in 'B' as shown in the diagram, 'not A' does not mean 'not B'.