6 ideas
15927 | Definition just needs negation, known variables, conjunction, disjunction, substitution and quantification [Weyl, by Lavine] |
Full Idea: For mathematics, Weyl arrived (by 1917) at a satisfactory list of definition principles: negation, identification of variables, conjunction, disjunction, substitution of constants, and existential quantification over the domain. | |
From: report of Hermann Weyl (works [1917]) by Shaughan Lavine - Understanding the Infinite V.3 | |
A reaction: Lavine summarises this as 'first-order logic with parameters'. |
9470 | Modal logic is not an extensional language [Parsons,C] |
Full Idea: Modal logic is not an extensional language. | |
From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.159 n8) | |
A reaction: [I record this for investigation. Possible worlds seem to contain objects] |
9469 | Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C] |
Full Idea: I argue (against Quine) that the existential quantifier substitutionally interpreted has a genuine claim to express a concept of existence, which may give the best account of linguistic abstract entities such as propositions, attributes, and classes. | |
From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.156) | |
A reaction: Intuitively I have my doubts about this, since the whole thing sounds like a verbal and conventional game, rather than anything with a proper ontology. Ruth Marcus and Quine disagree over this one. |
9468 | On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C] |
Full Idea: For the substitutional interpretation of quantifiers, a sentence of the form '(∃x) Fx' is true iff there is some closed term 't' of the language such that 'Ft' is true. For the objectual interpretation some object x must exist such that Fx is true. | |
From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.156) | |
A reaction: How could you decide if it was true for 't' if you didn't know what object 't' referred to? |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
Full Idea: Archelaus was the first person to say that the universe is boundless. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |