4 very easy arguments. Are they valid?

[DBT]

We’re dealing with two different issues. While I still maintain that a valid parking ticket and a valid deductive argument might seem to share a commonality, they don’t. Either way, the other issue might better be explained with this:

https://en.m.wikipedia.org/wiki/Principle_of_explosion

I agree with what the article says about 'the principle of explosion.' It's basically what I thought. I can't see much point to it though. Maybe as an exercise abstract philosophy, who knows......

 

[Angra Mainyu]

Angra is engaging in metaphysisn not logic.

No, I am doing logic, but correctly.

If you apply formal logic properly it does not matter what you call or describe it. The results of the conclusion does not vary.with interpretation.

Sure, though what conclusions you can derive depends on the logic (there are different logics, e.g., intuitionistic is weaker than classic), but I'm doing classical logic here, which is by far the most common and the most widely accepted - and the strongest in terms of what one can prove.

I would also defend it as the better fit for our language, but that would not strictly be logic.

It is like calculating 1 + 1 = 2 with the rules of arithmetic versus debating what addition 'means' conceptually.

No, I am telling you that your application of logic is mistaken.

A valid logical conclusion in the case of a syllogism is a conclusion that is a binary true or false traceable to the premises using the rules of logic.

P1 Jack is a dog
P2 Jack is not a dog
C Jack is a dog and Jack is not a dog.

Show with formal logic the conclusion follows from the premises.

That is easy. I only need to show that there is no assignment of values on which all of the premises are true, but the conclusion is false. Let us formalize:

P1: P
P2: ¬P.
C: P∧¬P.

The possible assignments of value for P are T or F. So, we have:

P:T

P1:T
P2:F
C:F

Not a problem, because on this assignment, not all of the premises are true (P2 is false), and thus, it is not the case that all of the premises are true but the conclusion is false.

Let us try the other possible assignment:

P:F

P1:F
P2:T
C:F

Not a problem, because on this assignment, not all of the premises are true (P1 is false), and thus, it is not the case that all of the premises are true but the conclusion is false.

Since there is no other possible assignment, this proves on classical logic that the conclusion follows from the premises.

 

[Angra Mainyu]

We’re dealing with two different issues. While I still maintain that a valid parking ticket and a valid deductive argument might seem to share a commonality, they don’t. Either way, the other issue might better be explained with this:

https://en.m.wikipedia.org/wiki/Principle_of_explosion

I agree with what the article says about 'the principle of explosion.' It's basically what I thought. I can't see much point to it though. Maybe as an exercise abstract philosophy, who knows......

The same principles of classical logic that are used widely in math, logic, philosophy, and other fields, also imply that. It can be useful when doing math exercises, but also being familiar with that may be helpful to better understand logic (e. g., just look at some of the exchanges in this thread) . At any rate, the OP arguments do not involve the Principle of Explosion.

 

[DBT]

We’re dealing with two different issues. While I still maintain that a valid parking ticket and a valid deductive argument might seem to share a commonality, they don’t. Either way, the other issue might better be explained with this:

https://en.m.wikipedia.org/wiki/Principle_of_explosion

I agree with what the article says about 'the principle of explosion.' It's basically what I thought. I can't see much point to it though. Maybe as an exercise abstract philosophy, who knows......

The same principles of classical logic that are used widely in math, logic, philosophy, and other fields, also imply that. It can be useful when doing math exercises, but also being familiar with that may be helpful to better understand logic (e. g., just look at some of the exchanges in this thread) . At any rate, the OP arguments do not involve the Principle of Explosion.

Yes, indeed. It is clear that the OP arguments do not involve the Principle of Explosion.