Combining Texts

All the ideas for 'The Case for Closure', 'The Thesis that Mathematics is Logic' and 'Nonexistent Objects'

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6 ideas

5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Putnam coined the term 'if-thenism' [Putnam, by Musgrave]
     Full Idea: Putnam coined the term 'if-thenism'.
     From: report of Hilary Putnam (The Thesis that Mathematics is Logic [1967]) by Alan Musgrave - Logicism Revisited §5 n
9. Objects / A. Existence of Objects / 4. Impossible objects
There is an object for every set of properties (some of which exist, and others don't) [Parsons,T, by Sawyer]
     Full Idea: According to Terence Parsons, there is an object corresponding to every set of properties. To some of those sets of properties there corresponds an object that exists, and to others there corresponds an object that does not exist (a nonexistent object).
     From: report of Terence Parsons (Nonexistent Objects [1980]) by Sarah Sawyer - Empty Names 5
     A reaction: This I take to be the main source of the modern revival of Meinong's notorious view of objects (attacked by Russell). I always find the thought 'a round square is square' to be true, and in need of a truthmaker. But must a round square be non-triangular?
11. Knowledge Aims / B. Certain Knowledge / 2. Common Sense Certainty
Commitment to 'I have a hand' only makes sense in a context where it has been doubted [Hawthorne]
     Full Idea: If I utter 'I know I have a hand' then I can only be reckoned a cooperative conversant by my interlocutors on the assumption that there was a real question as to whether I have a hand.
     From: John Hawthorne (The Case for Closure [2005], 2)
     A reaction: This seems to point to the contextualist approach to global scepticism, which concerns whether we are setting the bar high or low for 'knowledge'.
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure
How can we know the heavyweight implications of normal knowledge? Must we distort 'knowledge'? [Hawthorne]
     Full Idea: Those who deny skepticism but accept closure will have to explain how we know the various 'heavyweight' skeptical hypotheses to be false. Do we then twist the concept of knowledge to fit the twin desiderata of closue and anti-skepticism?
     From: John Hawthorne (The Case for Closure [2005], Intro)
     A reaction: [He is giving Dretske's view; Dretske says we do twist knowledge] Thus if I remember yesterday, that has the heavyweight implication that the past is real. Hawthorne nicely summarises why closure produces a philosophical problem.
We wouldn't know the logical implications of our knowledge if small risks added up to big risks [Hawthorne]
     Full Idea: Maybe one cannot know the logical consequences of the proposition that one knows, on account of the fact that small risks add up to big risks.
     From: John Hawthorne (The Case for Closure [2005], 1)
     A reaction: The idea of closure is that the new knowledge has the certainty of logic, and each step is accepted. An array of receding propositions can lose reliability, but that shouldn't apply to logic implications. Assuming monotonic logic, of course.
Denying closure is denying we know P when we know P and Q, which is absurd in simple cases [Hawthorne]
     Full Idea: How could we know that P and Q but not be in a position to know that P (as deniers of closure must say)? If my glass is full of wine, we know 'g is full of wine, and not full of non-wine'. How can we deny that we know it is not full of non-wine?
     From: John Hawthorne (The Case for Closure [2005], 2)
     A reaction: Hawthorne merely raises this doubt. Dretske is concerned with heavyweight implications, but how do you accept lightweight implications like this one, and then suddenly reject them when they become too heavy? [see p.49]