6 ideas
| 18253 | I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege] |
| Full Idea: You need a double transition, from cardinal numbes (Anzahlen) to the rational numbers, and from the latter to the real numbers generally. I wish to go straight from the cardinal numbers to the real numbers as ratios of quantities. | |
| From: Gottlob Frege (Letters to Russell [1902], 1903.05.21), quoted by Michael Dummett - Frege philosophy of mathematics 21 'Frege's' | |
| A reaction: Note that Frege's real numbers are not quantities, but ratios of quantities. In this way the same real number can refer to lengths, masses, intensities etc. |
| 18166 | The loss of my Rule V seems to make foundations for arithmetic impossible [Frege] |
| Full Idea: With the loss of my Rule V, not only the foundations of arithmetic, but also the sole possible foundations of arithmetic, seem to vanish. | |
| From: Gottlob Frege (Letters to Russell [1902], 1902.06.22) | |
| A reaction: Obviously he was stressed, but did he really mean that there could be no foundation for arithmetic, suggesting that the subject might vanish into thin air? |
| 14933 | Scientific properties are defined by the laws that embody them [Psillos, by Ladyman/Ross] |
| Full Idea: For Psillos, properties in mature science are defined by the laws in which they feature. | |
| From: report of Stathis Psillos (Scientific Realism [1999]) by J Ladyman / D Ross - Every Thing Must Go 3.5 | |
| A reaction: This is a perfect example of the Humean approach getting everything the wrong way round. Laws are not primitives from which we derive our account of nature - they are generalisations built up from the behaviour of prior properties. |
| 18269 | Logical objects are extensions of concepts, or ranges of values of functions [Frege] |
| Full Idea: How are we to conceive of logical objects? My only answer is, we conceive of them as extensions of concepts or, more generally, as ranges of values of functions ...what other way is there? | |
| From: Gottlob Frege (Letters to Russell [1902], 1902.07.28), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 7 epigr | |
| A reaction: This is the clearest statement I have found of what Frege means by an 'object'. But an extension is a collection of things, so an object is a group treated as a unity, which is generally how we understand a 'set'. Hence Quine's ontology. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |