Michael McCourt, who’s a grad student in the Philosophy Department at UMD and studies logic and language, spoke about semantic paradoxes. He assumed the background that I gave in my lecture last week, available in this post (and the linked papers).
NOTES are below (thanks to Hannah Tsai). Last week’s post should help with context. Slideshow hopefully coming soon.
- Semantic paradoxes
- (A) Epimenides the Crete says that all Cretans are liars.
- (A) is both true and false. This is bad.
This is both self referential and assumes bivalence
- (B) This sentence is not true
- Simple untruth liar, assume true or untrue instead of true or false
- Still self referential…
- (A) and (B) are semantically defective.
- (D) (D) is true.
- Not a paradox, but it adds nothing.
- Non-classic logic solution
- Generates a need for non-classical logic that says the Law of Excluded middle doesn’t hold for all sentences (there are more than two possibilities) and that contradictions can be both true and false but the principle of explosion doesn’t hold (Once a contradiction has been asserted, any proposition (or its negation) can be inferred from it.)
- Set theory solution
- Russell’s set theoretic paradox is resolved by limiting a set’s members to its n-1 stage.
- Tarski claims that the liar sentence isn’t a sentence by limiting applications of truth predicates to other languages. waht
- Contextualist solution
- (B) is semantically defective, but some are true and not true. It all depends on context.
- YABLO’S PARADOX
- Infinite sequence of sentences generating a paradox.