11 ideas
| 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. |
| 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. |
| 12312 | The real essence of a thing is its powers, or 'dispositional properties' [Copi] |
| Full Idea: With respect to scientific usage, we can say that the real essence of a thing will consist very largely of powers or, in modern terms, dispositional properties. | |
| From: Irving M. Copi (Essence and Accident [1954], p.718) | |
| A reaction: Once again, Copi is a hero. I personally love the word 'powers' in metaphysics (and dislike the word 'properties', which is lost in a fog of confusion). See Molnar on 'powers' and Mumford on 'dispositions'. |
| 10937 | Essential properties are the 'deepest' ones which explain the others [Copi, by Rami] |
| Full Idea: The 'explanatory characterization' says that the essential properties of an object are the object's deepest explanatory properties, which explain the other properties of the object - and which Copi claims is mind-independent. | |
| From: report of Irving M. Copi (Essence and Accident [1954]) by Adolph Rami - Essential vs Accidental Properties §2 | |
| A reaction: It is, of course, normal to see a good explanation as being dependent on the interests of the audience. Perhaps this account should be in terms of causal powers. See Shoemaker on properties. |
| 12308 | In modern science, nominal essence is intended to be real essence [Copi] |
| Full Idea: In the sphere of scientific enquiry the distinction between real and nominal essence tends to disappear; the scientist's classification of things is intended to be in terms of their real essences. | |
| From: Irving M. Copi (Essence and Accident [1954], p.716) | |
| A reaction: Thus we have disputes over what is the 'real' classification of natural kinds such as animals. There is not much point in a classification system that does not at least reflect some aspects of reality. |
| 12303 | Within the four types of change, essential attributes are those whose loss means destruction [Copi] |
| Full Idea: If we can distinguish the different kinds of change (alteration, locomotion, growth, diminution), then we can say that a given attribute is essential to an object if its loss would result in the destruction of that object. | |
| From: Irving M. Copi (Essence and Accident [1954], p.707-8) | |
| A reaction: As Copi is aware, this is a necessary condition for a property for essence, but not sufficient. If an attribute were necessary but non-essential, its loss would also be destruction. We say the essential attributes must also have some explanatory role. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 12307 | Modern science seeks essences, and is getting closer to them [Copi] |
| Full Idea: Modern science seeks to know the real essences of things, and its increasing successes seem to be bringing it progressively nearer to that goal. | |
| From: Irving M. Copi (Essence and Accident [1954], p.715) | |
| A reaction: This is from a notable pioneering paper, which outlined scientific essentialism even before Marcus and Kripke began to offer a modern account of essence to give it backing. Compare Popper, who thinks essences are will-o-the-wisps. |
| 12310 | Real essences are scientifically knowable, but so are non-essential properties [Copi] |
| Full Idea: Contrary to Locke, I should hold that real essences are in principle knowable, and contrary to Aristotle, I should hold that non-essential or accidental properties can also be objects of scientific knowledge. | |
| From: Irving M. Copi (Essence and Accident [1954], p.717) | |
| A reaction: Copi has just become my hero. Aristotle's account of definition is on the brink of allowing fine-tuned essences, but he thinks universal understanding blocks knowledge of individuals. But cross-referencing of universals pinpoints individuals. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |