12 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? |
| 12695 | Epicurean atomists say body is sensible, to distinguish it from space. [Garber] |
| Full Idea: The Epicurean atomists also defined body in terms of the property of being sensible, in order to distinguish it from empty space, which is not sensible. | |
| From: Daniel Garber (Leibniz:Body,Substance,Monad [2009], 1) | |
| A reaction: This is a very illuminating bit of background, for those of us who have the knee-jerk reaction that monadology is barking mad. |
| 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. |
| 7071 | Life and rationality are pointless if we can only contemplate the freedom of our own ego [Jacobi] |
| Full Idea: If the highest upon which I can reflect, what I can contemplate, is my empty and pure, naked and mere ego, with its autonomy and freedom: then rational self-contemplation, then rationality is for me a curse - I deplore my existence. | |
| From: Friedrich Jacobi (Letters to Fichte [1799], Ch.2), quoted by Simon Critchley - Continental Philosophy - V. Short Intro | |
| A reaction: This is a rebellion against Fichte's interpretation of Kant. It is a lovely cry from the heart on behalf of everyone who resents lines of philosophical thinking that seem to imprison the mind and cut us off from the ordinary world and real life. |
| 7072 | Jacobi was the first philosopher to talk of nihilism [Jacobi, by Critchley] |
| Full Idea: Jacobi was the first to philosophically employ the concept of nihilism. | |
| From: report of Friedrich Jacobi (Letters to Fichte [1799]) by Simon Critchley - Continental Philosophy - V. Short Intro Ch.2 | |
| A reaction: Critchley explains that it was Jacobi's fear that Fichte was drawing nihilist conclusions from Kant's philosophy. This fear may be seen as the beginning of what is loosely called 'continental philosophy'. A worthy subject for thinkers... |
| 12705 | Epicurean atoms are distinguished by their extreme hardness [Garber] |
| Full Idea: In Epicurean atomism (of Cordemoy, for example) there is a world of basic things distinguished by virtue of their extreme hardness. | |
| From: Daniel Garber (Leibniz:Body,Substance,Monad [2009], 2) | |
| A reaction: Garber says that Leibniz espouses 'substantial atomism', which is different from this. Leibniz's atoms have active power, where these atoms just embody total resistance. |