|One, number 1: in modern logic it is not possible to introduce the number one directly. It must be introduced indirectly, via existential quantification ("for at least one x ...") and universal quantification ("for all x ..."). In addition, identity is needed. See also definition, identity, logic, elementary logic, number theory, numbers._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
Def "exactly one" / logical form / Prior: to say that precisely an individual fs is to say that as for some x, x φs and for every x and y, if x φs and y φs, then x is the same individual as y. - Only with "φ-ing" instead of "F" (predicate).
Property/predicate/Prior: this uses "φ-ing" (digit verbs) instead of "F" (property). - But also
"Property to φ- ’- but" the property of the ()-ing forms not a noun of a verb. - But is part of the whole functor " ..is The same as .. "or the functor:" whatever ()s, ()s ".
This is not aproperty, otherwise false equivalence: "property that is applied to anything" could then falsely equate mermaids and Pegasi._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
Objects of thought Oxford 1971
Arthur N. Prior
Papers on Time and Tense 2nd Edition Oxford 2003