3-Valued Logic | Non-Classical Logic | Attic Philosophy

In classical logic, sentences are always either true or false (but never both). That rule breaks down in non-classical logic, and things get more interesting! In this video, we take a deeper look into three important 3-valued logics: Strong Kleene logic, Lukasiewitz logic, and the Logic of Paradox. This is a follow-up to my intro to non-classical logic:

00:00 - Intro
01:10 - Recap
01:38 - 3 logics
01:55 - Validity
02:17 - Strong Kleene logic
04:11 - Lukasiewitz logic
05:44 - Logic of Paradox
06:40 - Validity in LP
08:38 - Entailment
11:50 - Philosophical Uses

More videos on non-classical logic coming soon! If there’s a topic you’d like to see covered, leave me a comment below.

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#logic #philosophy #semantics

[brandonpropterhoc]

i am a philosophy major that just graduated and i love logic. that is my focus and i plan on getting my master and phd in logic. but i will say that i wish i was sponge and could just memorize what i learn. its going to take my a while to wrap my brain around all of this.

[xybersurfer]

nice video, i've been enjoying your channel. what do you mean with entailment and validity?

[Bunnokazooie]

Strong Kleene's "Other" feels a lot like a null pointer in programming.

[nametheunknown_]

Thanks again for this series. What a strange subject. In what way does any of this actually relate to reality I wonder? 🤔

[vitusschafftlein]

Thanks for the great video! I am curious about a few things:
1) If LP and FOL have the same set of valid sentences, then ⊨ (p ∧ ¬p) → q in LP because it is the case in FOL as well. But isn't a characteristic that this principle does not hold?
2) Am I right that the deduction theorem does not hold in LP? I think about it this way: Let's assume it does. Since LP and FOL have the same set of valid sentences and by the deduction theorem, you can transform every valid inference into a valid formula (and vice versa), the same inferences must hold. But this is not the case. So the deduction theorem does not hold.
3) Your videos on intuitionistic logic are so damn good that we're going to watch them together in my study group! We're still looking for a intermediate-friendly introduction - can you recommend one?
Keep up the good work!

[luisleon]

Thank you very much for your awesome videos. I notice in this video that (A -> A) is valid in the Tukasiewitz Logic, but (A V not A) is not. However, ( A -> A) is equivalent to (A V not A) according to definition of implication. So, we have Validity is equivalent to no Validity. It seems to me like a contradiction in the Tukasiewitz Logic or am I missing something?

[BelegaerTheGreat]

Yeah, Set Theory gets a stroke seeing that (3-valued) use of ¬.

[petarpejic]

I dont understand all of this yet but it seems as if when people say he did this to me so its ok when i do it to him, because he is evil. You cant be just good by oposing evil, you can be evil and opose evil or you cant just be unbiased and get to the truth you have to be biased towards truth to see it. When you are unbiased you arent seeig at all. Im not sure if thrse concepts apply in these cases but i get the vibe it does i feel like 1+1=2. In going to be dissapointed i think

[pyb.]

You need to work on pedagogy. What is it like to not know what you know? Work from there.