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### Shouldn't statements be considered equivalent based on their meaning rather than truth tables?

Consider the following truth table, which serves to define the logical connective ⇔, P | Q || P⇔Q T | T || T T | F || F F | T || F F | F || T According to the above truth table, the logical ...
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### Why is it that when A is false and B is false, we infer that A->B is true?

Why is it that when A is false and B is false, we infer that A->B is true? If A isn't true then we don't know if maybe when it is true then B would be false. could be B would be true, could be it'd ...
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### Why do contradictions imply anything?

I got this from the thread Why are conditionals with false antecedents considered true? And this is what Stefan Perko answered. Suppose it is raining and it is not raining. Then it is raining. ...
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### In basic logic, if an argument contains a self-contradictory premise, how come the argument is valid?

I have started to attend the logic lectures. The lecture notes indicate that a "self-contradiction" is a statement that is always false. But why will it lead to a valid statement?
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### Intuitively, why are Universal Statements true in the Empty Universe?

Source: p 165. Sweet Reason: A Field Guide to Modern Logic (2010 2 ed) by Henle, Garfield, Tymoczko. I read this on Math SE; please advise if it pertains to my simpler question.   One property of ...
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### How can one intuit that P → Q ≡ ¬P ∨ (P ∧ Q)?

I have not succeeded in intuiting P → Q ≡ ¬P ∨ Q in the sense of imagining how one would conjecture or divine the equivalence without any "foreknowledge" of ¬P ∨ Q to invoke formal proofs or truth ...
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### Can 'All S is P' ever be false if S is empty?

I'm self-learning logic, I'm stuck on an issue similar to this question: In modern logic, why does "All S is P" contradict "Some S is not P"? In the boolean interpretation 'All S ...
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### Do mathematicians take Modern Logic to be an appropriate representation of our sense of logic?

What examples do we have of mathematicians who explicitly and publicly expressed their personal confidence that mainstream modern logic, as used in mathematics, either as object of study in itself or ...
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