15 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. |
| 16728 | Logicians acknowledge too few things, while others acknowledge too many [Fitzralph] |
| Full Idea: Those who have been well trained in logic err in recognising too few things, whereas others who are ignorant of logic ascribe to every statement a new entity, postulating more entities than God has ever established as real. | |
| From: Richard Fitzralph (Sentences [1328], II.1.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 22.3 |
| 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. |
| 7301 | The phenomenalist says that to be is to be perceivable [Cardinal/Hayward/Jones] |
| Full Idea: Where the idealist says that to be (i.e. to exist) is to be perceived, the phenomenalist says that to be is to be perceivable. | |
| From: Cardinal/Hayward/Jones (Epistemology [2004], Ch.4) | |
| A reaction: This is a nice phenomenalist slogan to add to Mill's well known one (Idea 3583). Expressed in this form, it looks false to me. What about neutrinoes? They weren't at all perceivable until recently. Maybe some physical stuff can never be perceived. |
| 7302 | Linguistic phenomenalism says we can eliminate talk of physical objects [Cardinal/Hayward/Jones] |
| Full Idea: Linguistic phenomenalism argues that it is possible to remove all talk of physical objects from our speech with no loss of meaning. | |
| From: Cardinal/Hayward/Jones (Epistemology [2004], Ch.4) | |
| A reaction: I find this proposal unappealing. My basic objection is that I cannot understand why anyone would refuse to even contemplate the question of WHY I am having a given group of consistent experiences, of (say) a table kind. |
| 7303 | If we lack enough sense-data, are we to say that parts of reality are 'indeterminate'? [Cardinal/Hayward/Jones] |
| Full Idea: The problem with taking sense-data as basic is that some data can appear indeterminate. If we can't discern the colour of someone's eyes, or the number of sides of a complex figure, are we to say that there is no fact about those things? | |
| From: Cardinal/Hayward/Jones (Epistemology [2004], Ch.4) | |
| A reaction: I like that. How many electrons are there in the sun? Such things cannot just be reduced to talk of sense-data, as there is obviously a vast gap between the data and the facts. As usual, ontology and epistemology must be kept separate. |
| 7299 | Primary qualities can be described mathematically, unlike secondary qualities [Cardinal/Hayward/Jones] |
| Full Idea: All the primary qualities lend themselves readily to mathematical or geometric description. ...but it seems that secondary qualities are less amenable to being represented mathematically. | |
| From: Cardinal/Hayward/Jones (Epistemology [2004], Ch.4) | |
| A reaction: As a believer in the primary/secondary distinction, I welcome this point. This is either evidence for the external reality of primary qualities, or an interesting observation about maths. Do we make the primary/secondary distinction because we do maths? |
| 7300 | An object cannot remain an object without its primary qualities [Cardinal/Hayward/Jones] |
| Full Idea: An object cannot lack shape, size, position or motion and remain an object. | |
| From: Cardinal/Hayward/Jones (Epistemology [2004], Ch.4) | |
| A reaction: This points towards the essentialist view (see Idea 5453). This does raise the question of whether an object could lose its colour with impugnity, or the quality of sound that it makes when struck. |
| 7297 | My justifications might be very coherent, but totally unconnected to the world [Cardinal/Hayward/Jones] |
| Full Idea: My beliefs could be well justified in coherentist terms, while not accurately representing the world, and my system of beliefs could be completely free-floating. | |
| From: Cardinal/Hayward/Jones (Epistemology [2004], Ch.3) | |
| A reaction: This nicely encapsulates to correspondence objection to coherence theory. One thing missing from the coherence account is that beliefs aren't chosen for their coherence, but are mostly unthinkingly triggered by experiences. |