Combining Texts

All the ideas for 'The Problem of Empty Names', 'The iterative conception of Set' and 'Infinitism not solution to regress problem'

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

4 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
18192 Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy]
     Full Idea: For Boolos, the Replacement Axioms go beyond the iterative conception.
     From: report of George Boolos (The iterative conception of Set [1971]) by Penelope Maddy - Naturalism in Mathematics I.3
5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
18946 Unreflectively, we all assume there are nonexistents, and we can refer to them [Reimer]
     Full Idea: As speakers of the language, we unreflectively assume that there are nonexistents, and that reference to them is possible.
     From: Marga Reimer (The Problem of Empty Names [2001], p.499), quoted by Sarah Sawyer - Empty Names 4
     A reaction: Sarah Swoyer quotes this as a good solution to the problem of empty names, and I like it. It introduces a two-tier picture of our understanding of the world, as 'unreflective' and 'reflective', but that seems good. We accept numbers 'unreflectively'.
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
8836 Must all justification be inferential? [Ginet]
     Full Idea: The infinitist view of justification holds that every justification must be inferential: no other kind of justification is possible.
     From: Carl Ginet (Infinitism not solution to regress problem [2005], p.141)
     A reaction: This is the key question in discussing whether justification is foundational. I'm not sure whether 'inference' is the best word when something is evidence for something else. I am inclined to think that only propositions can be reasons.
8837 Inference cannot originate justification, it can only transfer it from premises to conclusion [Ginet]
     Full Idea: Inference cannot originate justification, it can only transfer it from premises to conclusion. And so it cannot be that, if there actually occurs justification, it is all inferential.
     From: Carl Ginet (Infinitism not solution to regress problem [2005], p.148)
     A reaction: The idea that justification must have an 'origin' seems to beg the question. I take Klein's inifinitism to be a version of coherence, where the accumulation of good reasons adds up to justification. It is not purely inferential.