Validity and necessary truths

Validity is defined in a couple of ways. I like to define it like this: An argument is valid iff the superconjunction1 of all the premises and the negation of the conclusion is impossible. It sounds a bit unusual at first but it is worded that way to prevent confusion about modalities. A more common…

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Truth tables and necessary truths

In the essay Validity and necessary truths I used truth tables with necessary truths and impossibilities in it. I did it like this: P □Q P→□Q T T T F T T Note that the modal operator is placed in the truth table also. It could also be done like this: P Q P→Q T…

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Logical impossibilities

What does impossible mean? Other than ‘not-possible’. Logical impossibility is the topic of this essay. More specifically we’re going to explore the two distinct meanings of logical impossible that I briefly mentioned in a previous essay A journey into possibility land.1 The two logical impossibilities The two kinds of logical impossibility are absolute and relative…

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Some modal fallacy whine

Given how much debate the modal fallacy have spawned on FRDB, it’s interesting to note how little two academics wrote about it when they encountered it while discussing knowledge skepticism: 2. If a belief could be mistaken, then it is not knowledge. “The phrase ‘could be mistaken’ is susceptible to a number of interpretations. According…

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A journey into possibility land

Intro and types I’ve been paying very close attention as of late to a special type of discourse: Namely, about what is possible and what is impossible. This study has led me to be very careful about my language use when speaking of such things because there are multiple types of possibilities: Logical, epistemic, physical,…

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Does a sound LPoE establish that god is impossible?

I’ve heard that claim, but do you think it is true? I don’t. All LPoEs (Logical Problem of Evil’s) can be seen as an inconsistent set of propositions. Here’s a really simple version: Simple LPoE: 1. God is all-good. 2. God is all-powerful. 3. God is all-knowledgeable. 4. If god is all-good, all-powerful and all-knowledgeable,…

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The modal fallacy

This is a translation of my earlier article on the subject. Link. The modal fallacy By Emil Kirkegaard, Deleet.dk This fallacy is rather common among persons who are not well versed in logic (especially modal logic). Consider these two not logically identical sentences: I) If there exists at least one subject S that knows which…

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