22 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? |
| 12270 | Being is one [Melissus, by Aristotle] |
| Full Idea: Being is one. | |
| From: report of Melissus (fragments/reports [c.443 BCE]) by Aristotle - Topics 104b23 | |
| A reaction: I can only really understand this in terms of physics, as the belief that ultimately there is one simple theory which explains everything. That project doesn't look terribly promising, despite the lovely simplifications of modern physics. |
| 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. |
| 8239 | If the King likes music then there is hope for the state [Mengzi (Mencius)] |
| Full Idea: If the King has a great fondness for music, then perhaps there is hope for the state of Ch'i. | |
| From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.B.1) | |
| A reaction: This seems to be Shakespeare's attitude to music as well. The general idea must be that love of music requires a selfless state of mind, where the mind revels in the beauty of something outside of itself. Respect is the desirable result. |
| 23398 | Human nature is naturally compassionate and good (as a 'sprout'), but people may not be good [Mengzi (Mencius), by Norden] |
| Full Idea: Mengzi does not claim that humans are innately good; he claims that human nature is innately good. …He says that 'the heart of compassion' (manifested when anyone sees a child about to fall into a well) is the 'sprout of benevolence'. | |
| From: report of Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE]) by Bryan van Norden - Intro to Classical Chinese Philosophy 6.II | |
| A reaction: There is a nice distinction here between the 'sprout' of human nature and the finished product. Seeds have the potential to produce tall healthy plants, but circumstances can warp them. |
| 23400 | Righteousness is extending the unthinkable, to reveal what must be done [Mengzi (Mencius)] |
| Full Idea: People all have things they will not do. To extend this reaction to that which they will do is righteousness. | |
| From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 7B31), quoted by Bryan van Norden - Intro to Classical Chinese Philosophy 6.IV | |
| A reaction: Very nice! Kekes points out the enormous importance of unthinkable deeds. Depravity is when the unthinkable gradually begins to look possible, which is probably a social phenomenon, a creeping cancer in a culture. |
| 23399 | Each correct feeling relies on an underlying virtue [Mengzi (Mencius)] |
| Full Idea: The heart of compassion is benevolence. The heart of disdain is righteousness. The heart of respect is propriety. The heart of approval and disapproval is wisdom. | |
| From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 6A6), quoted by Bryan van Norden - Intro to Classical Chinese Philosophy 6.III | |
| A reaction: 'Disdain' seems to be the response to anyone who is disrespectful. Note that wisdom concerns judgements. Respect seems to be more of a social convention than an actual concern for others. |
| 8235 | Should a coward who ran fifty paces from a battle laugh at another who ran a hundred? [Mengzi (Mencius)] |
| Full Idea: If two soldiers were fleeing from a battle, and one stopped after a hundred paces and the other stopped after a fifty paces, what would you think if the latter, as one who only ran fifty paces, were to laugh at the former who ran a hundred? | |
| From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.A.3) | |
| A reaction: A nice illustration, in my view, of the universality of truths about human virtue. In no culture would this laughter be appropriate. Nevertheless, there must be degrees of dishonour. Better to flee than join in with the likely winners. |
| 8240 | A true king shares his pleasure with the people [Mengzi (Mencius)] |
| Full Idea: If you shared your enjoyment of music or of hunting with the people, you would be a true King. | |
| From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.B.1) | |
| A reaction: I suspect that this is a great truth for dictators and traditional monarchs. One pictures the successful ones attending public entertainments, and allowing the public to see their own. Tyrants keep entertainment private. Nero is a counterexample! |
| 8237 | Extend the treatment of the old and young in your family to the rest of society [Mengzi (Mencius)] |
| Full Idea: Treat the aged of your own family in a manner befitting their venerable age and extend this treatment to the aged of other families. Treat your own young in a manner befitting their tender age, and extend this to the young of other families. | |
| From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.A.7) | |
| A reaction: This seems to me to articulate the ideal of communitarianism very nicely. Morality is not just about healthy adults in war and peace. It must include the children and the old. The values of the family are above the values of contracts and calculations. |
| 8241 | Only put someone to death if the whole population believes it is deserved [Mengzi (Mencius)] |
| Full Idea: When close attendants say a man deserves death, do not listen; when all the councillors say so, do not listen; when everyone says so, have the case investigated. If he is guilty, put him to death; he was put to death by the whole country. | |
| From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.B.7) | |
| A reaction: The jury system is a gesture in this direction. Compare Idea 95. In Mencius's time, no doubt, everyone believed that capital punishment was sometimes right. Nowadays, when many people (e.g. me) reject it, the procedure won't work. |
| 8238 | Seeking peace through war is like looking for fish up a tree [Mengzi (Mencius)] |
| Full Idea: Your desire to extend your territory by war, in order to bring peace, is like looking for fish by climbing a tree. | |
| From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.A.7) | |
| A reaction: Mencius had a flair for analogies. Just occasionally I suppose he might be wrong on this point, but I would think that experiments in the laboratory of history have shown that he is right in nearly all cases. |
| 8236 | Avoid the animals you are going to eat, as it is hard once you have got to know them [Mengzi (Mencius)] |
| Full Idea: Once a gentleman has seen animals alive, he cannot bear to see them die, and once having heard their cry, he cannot bear to eat their flesh. That is why the gentleman keeps his distance from the kitchen. | |
| From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.A.7) | |
| A reaction: If you applied this to a Gestapo officer and his victims, it would obviously be the epitome of wickedness. But it is complex. Compassion is expected when we encounter suffering, but we are not obliged to seek out suffering. Or are we? |
| 3059 | There is no real motion, only the appearance of it [Melissus, by Diog. Laertius] |
| Full Idea: There is no such thing as real motion, but there only appears to be such. | |
| From: report of Melissus (fragments/reports [c.443 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.4.3 |
| 5100 | The void is not required for change, because a plenum can alter in quality [Aristotle on Melissus] |
| Full Idea: There is no need for void to be the cause of all change, because it is perfectly possible for a plenum to alter qualitatively (which is something Melissus overlooked). | |
| From: comment on Melissus (fragments/reports [c.443 BCE]) by Aristotle - Physics 214a27 | |
| A reaction: In modern physics this presumably gives us fluctuations in a force field. Motion is like a cat being digested by a python. The atomist claim that emptiness is needed if anything is to move still has intuitive appeal. |
| 456 | Nothing could come out of nothing [Melissus] |
| Full Idea: If Nothing existed, in no way could anything come into being out of nothing. | |
| From: Melissus (fragments/reports [c.443 BCE], B1), quoted by (who?) - where? |