Combining Texts

All the ideas for 'Science and Method', 'The Putney Debates' and 'Deriving Kripkean Claims with Abstract Objects'

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4 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry
10245 One geometry cannot be more true than another [Poincaré]
     Full Idea: One geometry cannot be more true than another; it can only be more convenient.
     From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics
     A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate.
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
10558 Abstract objects are actually constituted by the properties by which we conceive them [Zalta]
     Full Idea: Where for ordinary objects one can discover the properties they exemplify, abstract objects are actually constituted or determined by the properties by which we conceive them. I use the technical term 'x encodes F' for this idea.
     From: Edward N. Zalta (Deriving Kripkean Claims with Abstract Objects [2006], 2 n2)
     A reaction: One might say that whereas concrete objects can be dubbed (in the Kripke manner), abstract objects can only be referred to by descriptions. See 10557 for more technicalities about Zalta's idea.
18. Thought / E. Abstraction / 2. Abstracta by Selection
10557 Abstract objects are captured by second-order modal logic, plus 'encoding' formulas [Zalta]
     Full Idea: My object theory is formulated in a 'syntactically second-order' modal predicate calculus modified only so as to admit a second kind of atomic formula ('xF'), which asserts that object x 'encodes' property F.
     From: Edward N. Zalta (Deriving Kripkean Claims with Abstract Objects [2006], p.2)
     A reaction: This is summarising Zalta's 1983 theory of abstract objects. See Idea 10558 for Zalta's idea in plain English.
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
23215 Even the poorest have a life to lead, and so should consent to who governs them [-]
     Full Idea: For really I think that the poorest hee that is in England hath a life to live, as the greatest hee; …and every Man that is to live under a Government ought first by his own Consent to put himself under that Government.
     From: - (The Putney Debates [1647])
     A reaction: [remark made by Thomas Rainsborough] This is the social contract idea which is explicit in Hobbes. I'm sure we can at least trace it back to John Lilburne in the 1630s.