5
votes
Strong Completenss vs Finitely Strong Completenss
The canonical example of this is the logic $L(Q)$ gotten by adding the quantifier $Q\equiv$ "There exist uncountably many" to first-order logic. Improving on earlier work of Vaught, Keisler ...
- 251k
2
votes
Proof of the principle of explosion
Re the second point in your question, the proof still holds.
We have (1) $P$ and (2) $¬P$ as assumptions.
Instead of deriving (3) $P \lor Q$ from (1) by Disjunction introduction (aka: Addition), we ...
- 95.2k
1
vote
Accepted
How can a problem with cases be represented formally?
Naïm Favier's comment is spot-on.
First: A person who always tells the truth is called a "knight". It's quicker to say and to understand "$A$ is a knight" than to say or ...
1
vote
Meta-logic of Hilbert-style propositional calculus
Basically, we have two methods in logic to specify an axiomatic system:
Either we enumerate axioms and inference rules, defining uniform/simultaneous substitution as a syntactic rule or a metatheorem; ...
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