|Geach, Peter T.
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Negation/Geach: the problem with compound expressions is always the negation (with "all", "some").
Negation/Geach: in the subject-predicate-sentence: Negation is only possible from the predicate, not from the subject. - Modernity: quantification: also the negation of "there is" is possible. - New: also subject negation is possible: E.g. "not everyone is ..."
Negation/Russell: cannot be applied as a primitive term to propositions, therefore: All x are F: Negation: some x are not F "- Negation: not via a sentence: "Do not open the door" is on the same level as "Open the door".
Negation is not "logical secondary". - asymmetry: only with identifying predicates: e.g. the same man/not the same man - subject negation: "not everyone is ..." - predicate negation: Socrates is not ... "- negation is not parasitic to affirmation - no added meaning - Otherwise there would be a summation with double negation.
Negation/assertion/Geach: propositions can be put forward without asserting them. For example, "p > q" therefore we need a negation which is not polar to the assertion.
Logic Matters Oxford 1972