Combining Texts

All the ideas for 'works', 'Medical Conceptions of Health pre-Renaissance' and 'Letters to Russell'

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6 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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?
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
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.
22. Metaethics / B. Value / 2. Values / d. Health
22237 The Greeks had a single word meaning both 'beautiful' and 'good' [Pormann]
     Full Idea: The later Greeks coined the term 'kalokagathia' for the fact of being both beautiful [kalos] and good [agathos], thus linking moral and physical health.
     From: Peter E. Pormann (Medical Conceptions of Health pre-Renaissance [2019], p.44)
     A reaction: In their literature good people are often handsome, and bad people ugly. Socrates was famous for being an exception.
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
16713 Philosophers are the forefathers of heretics [Tertullian]
     Full Idea: Philosophers are the forefathers of heretics.
     From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
6610 I believe because it is absurd [Tertullian]
     Full Idea: I believe because it is absurd ('Credo quia absurdum est').
     From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2
     A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though.