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Background ideas -- Consequences -- Relations of support -- Logical consequence : the basic recipe -- Valid arguments and truth -- Language, form, and logical theories -- Language -- Atoms, connectives, and molecules -- Connectives and form -- Validity and form -- Language and formal languages -- Logical theories : rivalry -- Set-theoretic tools -- Sets -- Ordered sets : pairs and n-tuples -- Relations -- Functions -- Sets as tools -- Basic connectives -- Classical theory -- Cases : complete and consistent -- Classical truth conditions -- Basic classical consequence -- Motivation : precision -- Defined connectives -- Some notable valid forms -- A paracomplete theory -- Apparent unsettledness -- Cases : incomplete -- Paracomplete truth and falsity conditions -- Paracomplete consequence -- Defined connectives -- Some notable forms -- A paraconsistent theory -- Apparent overdeterminacy -- Cases : inconsistent -- Paraconsistent truth conditions -- Paraconsistent consequence -- Defined connectives -- Some notable forms -- Innards, identity, and quantifiers -- Atomic innards -- Atomic innards : names and predicates -- Truth and falsity conditions for atomics -- Cases, domains, and interpretation functions -- Classical, paracomplete, and paraconsistent -- Identity -- Logical expressions and logical form -- Validity involving identity -- Identity : informal sketch -- Truth conditions : informal sketch -- Everything and something -- Validity involving quantifiers -- Quantifiers : an informal sketch -- Truth and falsity conditions -- Paraconsistent, paracomplete, classical -- Freedom, necessity, and beyond -- Speaking freely -- Speaking of non-existent things -- Existential import -- Freeing our terms, expanding our domains -- Truth conditions : an informal sketch -- Possibilities -- Possibility and necessity -- Towards truth and falsity conditions -- Cases and consequence -- Remark on going beyond possibility -- Glimpsing different logical roads -- Other conditionals -- Other negations -- Other alethic modalities : actuality -- Same connectives, different truth conditions -- Another road to difference : consequence. |
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