Combining Texts

All the ideas for 'Set Theory and related topics (2nd ed)', 'Introduction to a Secret Encyclopaedia' and 'The Theory of Epistemic Rationality'

unexpand these ideas     |    start again     |     specify just one area for these texts


4 ideas

1. Philosophy / F. Analytic Philosophy / 2. Analysis by Division
Analysing right down to primitive concepts seems beyond our powers [Leibniz]
     Full Idea: An analysis of concepts such that we can reach primitive concepts...does not seem to be within human power.
     From: Gottfried Leibniz (Introduction to a Secret Encyclopaedia [1679], C513-14), quoted by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz
     A reaction: Leibniz is nevertheless fully committed, I think, to the existence of such primitives, and is in the grip of the rationalist dream that thoughts can become completely clear, and completely well-founded.
3. Truth / A. Truth Problems / 8. Subjective Truth
We hold a proposition true if we are ready to follow it, and can't see any objections [Leibniz]
     Full Idea: A proposition is held to be true by us when our mind is ready to follow it and no reason for doubting it can be found.
     From: Gottfried Leibniz (Introduction to a Secret Encyclopaedia [1679], p.7)
     A reaction: This follows on from Descartes' view, but it now sounds more like psychology than metaphysics. Clearly a false proposition could fit this desciption. Personally I follow propositions to which I can see no objection, without actually holding them true.
4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes
Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz]
     Full Idea: A relation R on a non-empty set S is an equivalence relation if it is reflexive (for each member a, aRa), symmetric (if aRb, then bRa), and transitive (aRb and bRc, so aRc). It tries to classify objects that are in some way 'alike'.
     From: Seymour Lipschutz (Set Theory and related topics (2nd ed) [1998], 3.9)
     A reaction: So this is an attempt to formalise the common sense notion of seeing that two things have something in common. Presumably a 'way' of being alike is going to be a property or a part
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
Rational internal belief is conviction that a proposition enhances a belief system [Foley, by Vahid]
     Full Idea: In Foley's subjective internalist account it is egocentrically rational for an agent to believe a proposition only if he would think on deep reflection that believing it is conducive to having an accurate and comprehensive belief system.
     From: report of Richard Foley (The Theory of Epistemic Rationality [1987], 2.1 B) by Hamid Vahid - Externalism/Internalism
     A reaction: I like this idea, because it indicates the link between internalism and coherence about justification. I don't think you can be an externalist coherence theorist for justification. [Reminder: Paul Thagard is the best writer on coherence].