# Tag Info

### Why should I not believe there are true contradictions?

Perhaps we should first check whether the statement, "No contradiction can be true," can be made more precise. We will say, "Propositions (A) and (not A) cannot both be true." But ...
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### Why should I not believe there are true contradictions?

All rules of logic are based on "intuition" in the sense you're using the word here. They are based on people agreeing, "This makes sense." There is no way to prove these rules ...
• 293

### Why should I not believe there are true contradictions?

It is a flaw in logic itself. It's funny I just made a similar post. Edit: Logic is a type of language that cannot tolerate contradiction. This is why the word "wulture" does not make sense ...

### Why should I not believe there are true contradictions?

You won't be able to refute any claims made by trivialists. Suppose some claim Q is false by direct proof. You mention this to a trivialist. They reply, "Oh, Q is true." They also say, "...
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### Why should I not believe there are true contradictions?

This got me thinking: How does one really justify the law of non-contradiction without just appealing to intuition? If you accept logic, but specifically deny the law of non contradiction, the ...
• 3,469

### Why should I not believe there are true contradictions?

Frame challenge: This is based on a false premise Your problem is a lot simpler than you think, and your YouTube reference is trivially wrong. You're only confused because they're talking rubbish, and ...
• 2,360

### Why should I not believe there are true contradictions?

I'll bite on the word belief which you are using in the title. SEP has a lot to say about Belief, but what strikes me as most important is that a belief is something that lives in the brain/mind. Also,...
• 2,887
1 vote

### Why should I not believe there are true contradictions?

Consider the English statement, A = "My eyes are closed." It denotes/symbolizes/represents/names some single proposition, out of the infinity of propositions. Now, some propositions have a ...
• 729
Accepted

### Why should I not believe there are true contradictions?

You may cancel from ordinary logic the prinicple of non-contradiction and admit at least one contradictory statement ’A and non-A’. But then you get for arbitrary statements B the valid statement A ...
• 33.1k
1 vote
Accepted

### Vacuous truth in non-classical logics

Does the notion of a vacuous truth exist in non-classical logics as well? The short answer is yes, ex falso quodlibet does hold constructively (constructively as in no axioms at all, neither ...
Accepted

### Relationship between Structural Contraction and the Absorption theorem?

Suppose we have a logic with a derivability relation ⊢ and a conditional → that obeys the deduction theorem for that logic, i.e. Γ ∪ {A} ⊢ B if and only if Γ ⊢ A → B Where Γ is a set of ...
• 26k
1 vote

### Relationship between Structural Contraction and the Absorption theorem?

As I understand your question, you want to know what role if any LSC plays in proving the Absorption theorem. The following proof uses the deduction theorem. Theorem: ⊢ (A → (A → B)) → (A → B) Proof. ...
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