14 ideas
| 9470 | Modal logic is not an extensional language [Parsons,C] |
| Full Idea: Modal logic is not an extensional language. | |
| From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.159 n8) | |
| A reaction: [I record this for investigation. Possible worlds seem to contain objects] |
| 13418 | 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. |
| 9469 | Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C] |
| Full Idea: I argue (against Quine) that the existential quantifier substitutionally interpreted has a genuine claim to express a concept of existence, which may give the best account of linguistic abstract entities such as propositions, attributes, and classes. | |
| From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.156) | |
| A reaction: Intuitively I have my doubts about this, since the whole thing sounds like a verbal and conventional game, rather than anything with a proper ontology. Ruth Marcus and Quine disagree over this one. |
| 9468 | On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C] |
| Full Idea: For the substitutional interpretation of quantifiers, a sentence of the form '(∃x) Fx' is true iff there is some closed term 't' of the language such that 'Ft' is true. For the objectual interpretation some object x must exist such that Fx is true. | |
| From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.156) | |
| A reaction: How could you decide if it was true for 't' if you didn't know what object 't' referred to? |
| 17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
| Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal. | |
| From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3 | |
| A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'. |
| 18201 | General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C] |
| Full Idea: The existence of very general principles in mathematics are universally regarded as obvious, where on an empiricist view one would expect them to be bold hypotheses, about which a prudent scientist would maintain reserve. | |
| From: Charles Parsons (Mathematical Intuition [1980], p.152), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: This is mainly aimed at Quine's and Putnam's indispensability (to science) argument about mathematics. |
| 13419 | 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? |
| 13417 | 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. |
| 13795 | Properties only have identity in the context of their contraries [Elder] |
| Full Idea: The very being, the identity, of any property consists at least in part in its contrasting as it does with its own proper contraries. | |
| From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 2.4) | |
| A reaction: See Elder for the details of this, but the idea that properties can only be individuated contextually sounds promising. |
| 13798 | Maybe we should give up the statue [Elder] |
| Full Idea: Some contemporary metaphysicians infer that one of the objects must go, namely, the statue. | |
| From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 7.2) | |
| A reaction: [He cites Zimmerman 1995] This looks like a recipe for creating a vast gulf between philosophers and the rest of the population. If it is right, it makes the true ontology completely useless in understanding our daily lives. |
| 13797 | The loss of an essential property means the end of an existence [Elder] |
| Full Idea: The loss of any essential property must amount to the end of an existence. | |
| From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 3) | |
| A reaction: This is orthodoxy for essentialists, and I presume that Aristotle would agree, but I have a problem with the essence of a great athlete, who then grows old. Must we say that they lose their identity-as-an-athlete? |
| 13794 | Essential properties by nature occur in clusters or packages [Elder] |
| Full Idea: Essential properties by nature occur in clusters or packages. | |
| From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 2.2) | |
| A reaction: Elder proposes this as his test for the essentialness of a property - his Test of Flanking Uniformities. A nice idea. |
| 13796 | Essential properties are bound together, and would be lost together [Elder] |
| Full Idea: The properties of any essential nature are bound together....[122] so any case in which one of our envisioned familiar objects loses one of its essential properties will be a case in which it loses several. | |
| From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 3) | |
| A reaction: This sounds like a fairly good generalisation rather than a necessary truth. Is there a natural selection for properties, so that only the properties which are able to bind to others to form teams are able to survive and flourish? |
| 16591 | Prime matter is nothing but its parts [Vanini] |
| Full Idea: The whole of prime matter, considered as prime matter, is nothing other than its parts. | |
| From: Julio Cesare Vanini (Amphitheatrum [1615], Ex 5:p.28), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.2 | |
| A reaction: This is a late scholastic writer rejecting the traditional (and obscure) prime matter with the new corpuscularian approach. It signals the end of the Greek concept of matter. |