Combining Texts

All the ideas for 'fragments/reports', 'Intros to Russell's 'Essays in Analysis'' and 'Euthydemus'

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10 ideas

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / b. Cantor's paradox
Sets always exceed terms, so all the sets must exceed all the sets [Lackey]
     Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets.
     From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127)
     A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom.
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey]
     Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1.
     From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127)
     A reaction: Formulated by Burali-Forti in 1897.
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
Beautiful things must be different from beauty itself, but beauty itself must be present in each of them [Plato]
     Full Idea: Are fine things different from or identical to fineness? They are different from fineness itself, but fineness itself is in a sense present in each of them.
     From: Plato (Euthydemus [c.379 BCE], 301a)
11. Knowledge Aims / A. Knowledge / 1. Knowledge
Knowing how to achieve immortality is pointless without the knowledge how to use immortality [Plato]
     Full Idea: If there exists the knowledge of how to make men immortal, but without the knowledge of how to use this immortality, there seems to be no value in it.
     From: Plato (Euthydemus [c.379 BCE], 289b)
     A reaction: I take this to be not a gormless utilitarianism about knowledge, but a plea for holism, that knowledge only has value as part of some larger picture. The big view is the important view. He's wrong, though. Work out the use later.
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
Say how many teeth the other has, then count them. If you are right, we will trust your other claims [Plato]
     Full Idea: If each of you says how many teeth the other has, and when they are counted we find you do know, we will believe your other claims as well.
     From: Plato (Euthydemus [c.379 BCE], 294c)
     A reaction: This is the clairvoyant problem for reliabilism, if truth is delivered for no apparent reason. Useful, but hardly knowledge. HOW did you know the number of teeth?
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
What knowledge is required to live well? [Plato]
     Full Idea: What knowledge would enable us to live finely for the rest of our lives?
     From: Plato (Euthydemus [c.379 BCE], 293a)
     A reaction: A successful grasp of other people's points of view might lead to respect for them. Also a realisation that we are not isolated individuals. We really are all in it together.
22. Metaethics / C. The Good / 1. Goodness / e. Good as knowledge
Only knowledge of some sort is good [Plato]
     Full Idea: Nothing is good except knowledge of some sort.
     From: Plato (Euthydemus [c.379 BCE], 292b)
     A reaction: I've heard it suggested that truth is the only value. This is the Socratic idea that moral goodness is a matter of successful rational judgement. Not convinced, but interesting.
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
Something which lies midway between two evils is better than either of them [Plato]
     Full Idea: Something which is composed of two factors which are bad for different purposes and lies midway between them is better than either of the factors.
     From: Plato (Euthydemus [c.379 BCE], 306a)
25. Social Practice / E. Policies / 5. Education / b. Education principles
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.
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
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.