# Thread: 4 very easy arguments. Are they valid?

1. Originally Posted by fast
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......

2. Originally Posted by steve bank
Angra is engaging in metaphysisn not logic.
No, I am doing logic, but correctly.

Originally Posted by steve bank
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.

Originally Posted by steve bank

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.

Originally Posted by steve bank
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.

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