# Tag Info

## Hot answers tagged propositional-calculus

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### Why isn’t ‘because’ a logical connective in propositional logic?

It is because 'because' is not truth-functional. That is, knowing the truth-values of $P$ and $Q$ does not tell you the truth-value of '$P$ because of $Q$' For example, the two statements 'Grass is ...
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### "Modus moron" rule of inference?

It's true that if $P$ is false then $P\Rightarrow Q$ is true. But the question is not asking if $P\Rightarrow Q$ is true, it's asking you if you can infer $P$ from $P\Rightarrow Q$ and $Q$. Let's be ...
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### Why are proofs not written as collections of logic symbols but are instead written in sentences?

You have not translated the pages from Apostol's book into mathematical logic. What you have done is to transcribe them into your own idiosyncratic shorthand, which may be useful to you but is less ...
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### What is meant by "logically incorrect"?

Rather than assume what the author means, I consulted the textbook (p. $155$) and examined the excerpt in context... "Logic is the process of deducing information correctly -- it is not the ...
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### "Modus moron" rule of inference?

This pattern is a logical fallacy called Affirming the Consequent, though I often call it Modus Bogus. To show it is not a valid inference, here is a simple Refutation by Logical Analogy: If I have ...
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### Still struggling to understand vacuous truths

Given that we want the $\rightarrow$ to capture the idea of an 'if .. then ..' statement, it seems reasonable to insist that $P \rightarrow P$ is a True statement, no matter what $P$ is, and thus no ...
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### Does the unique existential quantifier commute with the existential quantifier?

No, they do not commute. Consider for example the nonnegative reals as a linear order. Then $$\exists x\exists !y(y\le x)$$ is true (take $x=0$), but $$\exists!y \exists x(y\le x)$$ is false since ...
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### What is the logical flaw in this reasoning? Abusing $T \equiv T \vee F$.
I will focus on your problem with $T\iff T\lor F$. Sure, under assumption that some formula $A(x)$ depending on a parameter $x$ is true (independent of the value for $x$), you may use that to deduce ...