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All the ideas for 'Review of Tait 'Provenance of Pure Reason'', 'The Barcan Formula and Metaphysics' and 'What is a Leading Principle?'

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8 ideas

4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The Barcan Formulas express how to combine modal operators with classical quantifiers [Simchen]
     Full Idea: The Barcan Formula and its converse gives expression to the most straightforward way of combining modal operators with classical quantification.
     From: Ori Simchen (The Barcan Formula and Metaphysics [2013], §1)
The Barcan Formulas are orthodox, but clash with the attractive Actualist view [Simchen]
     Full Idea: The Barcan Formulas are a threat to 'actualism' in modal metaphysics, which seems regrettable since the Formulas are validated by standard modal logics, but clash with the plausible and attractive actualist view (that there are no merely possible things).
     From: Ori Simchen (The Barcan Formula and Metaphysics [2013], §1)
     A reaction: He notes that the Barcan Formulas 'appear to require quantification over possibilia'. So are you prepared to accept the 'possible elephant in your kitchen'? Conceptually yes, but actually no, I would have thought. So possibilia are conceptual.
BF implies that if W possibly had a child, then something is possibly W's child [Simchen]
     Full Idea: In accordance with the Barcan Formula we assume that if it is possible that Wittgenstein should have had a child, then something or other is possibly Wittgentein's child.
     From: Ori Simchen (The Barcan Formula and Metaphysics [2013], §5)
     A reaction: Put like this it sounds unpersuasive. What is the something or other? Someone else's child? A dustbin? A bare particular? Wittgenstein's child? If it was the last one, how could it be Wittgenstein's child while only possibly being that thing?
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C]
     Full Idea: The difficulties historically attributed to the axiom of choice are probably better ascribed to the law of excluded middle.
     From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2)
     A reaction: The law of excluded middle was a target for the intuitionists, so presumably the debate went off in that direction.
6. Mathematics / C. Sources of Mathematics / 8. Finitism
If functions are transfinite objects, finitists can have no conception of them [Parsons,C]
     Full Idea: The finitist may have no conception of function, because functions are transfinite objects.
     From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §4)
     A reaction: He is offering a view of Tait's. Above my pay scale, but it sounds like a powerful objection to the finitist view. Maybe there is a finitist account of functions that could be given?
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C]
     Full Idea: If experience shows that some aspect of the physical world fails to instantiate a certain mathematical structure, one will modify the theory by sustituting a different structure, while the original structure doesn't lose its status as part of mathematics.
     From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2)
     A reaction: This seems to be a beautifully simple and powerful objection to the Quinean idea that mathematics somehow only gets its authority from physics. It looked like a daft view to begin with, of course.
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
Serious Actualism says there are no facts at all about something which doesn't exist [Simchen]
     Full Idea: Serious Actualism is the view that in possible circumstances in which something does not exist there are no facts about it of any kind, including its very non-existence
     From: Ori Simchen (The Barcan Formula and Metaphysics [2013], §1 n4)
     A reaction: He suggests that the Converse Barcan Formula implies this view. It sounds comparable to the view of Presentism about time, that no future or past truthmakers exist right now. If a new square table were to exist, it would have four corners.
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
A 'belief' is a habit which determines how our imagination and actions proceed [Peirce]
     Full Idea: A cerebral habit of the highest kind, which will determine what we do in fancy as well as what we do in action, is called a 'belief'.
     From: Charles Sanders Peirce (What is a Leading Principle? [1880], I)